//design no.20
 ablox:=
[
    { 10, 11, 13, 16, 18, 20, 22, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 14, 15, 17, 19, 21, 24, 26 },
    { 4, 5, 7, 16, 17, 19, 22, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 15, 18, 20, 21, 23, 26 },
    { 4, 5, 7, 10, 11, 14, 21, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 9, 12, 13, 22, 24, 25 },
    { 4, 5, 7, 9, 12, 13, 15, 18, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 11, 14, 16, 17, 19 },
    { 2, 4, 6, 12, 14, 17, 20, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 13, 18, 19, 24, 26 },
    { 2, 4, 6, 10, 13, 15, 19, 22, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 9, 14, 16, 20, 21, 25 },
    { 2, 4, 6, 9, 11, 16, 18, 21, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 10, 12, 15, 17, 22, 23 },
    { 2, 3, 7, 12, 13, 16, 19, 21, 23 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 6, 11, 14, 15, 20, 22, 24 },
    { 2, 3, 7, 9, 11, 17, 20, 22, 26 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 5, 6, 10, 12, 18, 19, 21, 25 },
    { 2, 3, 7, 10, 14, 15, 18, 24, 25 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 5, 6, 9, 13, 16, 17, 23, 26 },
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 6, 7, 9, 11, 15, 19, 23, 25, 27 },
    { 1, 3, 4, 13, 14, 17, 18, 21, 22 },
    { 2, 5, 8, 9, 14, 18, 19, 22, 23 },
    { 6, 7, 10, 13, 17, 20, 21, 24, 27 },
    { 1, 3, 4, 11, 12, 15, 16, 25, 26 },
    { 2, 5, 8, 11, 13, 15, 17, 21, 25 },
    { 6, 7, 12, 14, 16, 18, 22, 26, 27 },
    { 1, 3, 4, 9, 10, 19, 20, 23, 24 }
];
 //aff geom design inside
 blos:=
[
    { 1, 7, 8, 9, 14, 16, 20, 21, 25 },
    { 3, 6, 8, 10, 11, 14, 16, 17, 19 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 3, 6, 8, 9, 12, 13, 22, 24, 25 },
    { 3, 6, 8, 15, 18, 20, 21, 23, 26 },
    { 1, 5, 6, 9, 14, 15, 17, 24, 26 },
    { 1, 3, 4, 10, 12, 16, 20, 24, 26 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 2, 4, 6, 12, 14, 17, 20, 23, 25 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 2, 3, 7, 12, 14, 15, 19, 21, 24 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 2, 4, 6, 10, 13, 15, 19, 22, 26 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 9, 12, 13, 16, 17, 19, 21, 23, 26 },
    { 4, 5, 7, 16, 17, 19, 22, 24, 25 },
    { 1, 3, 4, 11, 13, 15, 17, 21, 25 },
    { 2, 5, 8, 10, 13, 17, 20, 21, 24 },
    { 4, 5, 7, 10, 11, 14, 21, 23, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 4, 5, 7, 9, 12, 13, 15, 18, 20 },
    { 2, 5, 8, 12, 14, 16, 18, 22, 26 },
    { 1, 3, 4, 9, 14, 18, 19, 22, 23 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 2, 3, 7, 9, 11, 17, 20, 22, 26 },
    { 1, 7, 8, 11, 13, 18, 19, 24, 26 },
    { 2, 5, 8, 9, 11, 15, 19, 23, 25 },
    { 2, 3, 7, 10, 13, 16, 18, 23, 25 },
    { 1, 7, 8, 10, 12, 15, 17, 22, 23 },
    { 1, 5, 6, 10, 12, 18, 19, 21, 25 },
    { 1, 5, 6, 11, 13, 16, 20, 22, 23 },
    { 2, 4, 6, 9, 11, 16, 18, 21, 24 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 }
];
/*> dc:=descode(27,blos,3);ac:=descode(27,ablox,3); 
> Dim(ac),Dim(dc),Dim(ac meet dc);
12 10 10

load "AD15-20.m";
Loading "AD15-20.m"
> od3:=od20;
> load "AD.m";     
Loading "AD.m"
3-rank design= 12
weight distribution code= [ <0, 1>, <6, 36>, <9, 366>, <12, 14904>, <15, 119808>, 
<18, 255360>, <21, 131220>, <24, 9594>, <27, 152> ]
no of constant weight-9's 75
75
2-(27, 9, 4) Design with 39 blocks
*/ //design no. 21
 ablox:=
[
    { 10, 12, 13, 16, 18, 19, 21, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 11, 14, 15, 17, 20, 22, 24, 26 },
    { 4, 5, 7, 16, 17, 19, 22, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 15, 18, 20, 21, 23, 26 },
    { 4, 5, 7, 10, 11, 14, 21, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 9, 12, 13, 22, 24, 25 },
    { 4, 5, 7, 9, 12, 13, 15, 18, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 11, 14, 16, 17, 19 },
    { 2, 4, 6, 12, 14, 17, 20, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 13, 18, 19, 24, 26 },
    { 2, 4, 6, 10, 13, 15, 19, 22, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 9, 14, 16, 20, 21, 25 },
    { 2, 4, 6, 9, 11, 16, 18, 21, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 10, 12, 15, 17, 22, 23 },
    { 2, 3, 7, 11, 13, 16, 20, 22, 23 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 6, 12, 14, 15, 19, 21, 24 },
    { 2, 3, 7, 9, 12, 17, 19, 21, 26 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 5, 6, 10, 11, 18, 20, 22, 25 },
    { 2, 3, 7, 10, 14, 15, 18, 24, 25 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 5, 6, 9, 13, 16, 17, 23, 26 },
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 6, 7, 9, 11, 15, 19, 23, 25, 27 },
    { 1, 3, 4, 13, 14, 17, 18, 21, 22 },
    { 2, 5, 8, 9, 14, 18, 19, 22, 23 },
    { 6, 7, 10, 13, 17, 20, 21, 24, 27 },
    { 1, 3, 4, 11, 12, 15, 16, 25, 26 },
    { 2, 5, 8, 11, 13, 15, 17, 21, 25 },
    { 6, 7, 12, 14, 16, 18, 22, 26, 27 },
    { 1, 3, 4, 9, 10, 19, 20, 23, 24 }
];
//aff geom design in code
 blos:=
[
    { 4, 5, 7, 21, 22, 23, 24, 25, 26 },
    { 3, 6, 8, 9, 12, 13, 22, 24, 25 },
    { 1, 5, 6, 11, 13, 16, 20, 22, 23 },
    { 1, 2, 16, 17, 19, 22, 24, 25, 27 },
    { 3, 6, 8, 15, 16, 17, 18, 19, 20 },
    { 2, 4, 6, 9, 14, 16, 20, 21, 25 },
    { 3, 6, 8, 10, 11, 14, 21, 23, 26 },
    { 6, 7, 10, 12, 16, 20, 24, 26, 27 },
    { 1, 7, 8, 9, 10, 15, 16, 21, 22 },
    { 3, 5, 9, 11, 16, 18, 21, 24, 27 },
    { 6, 7, 9, 11, 15, 19, 23, 25, 27 },
    { 9, 12, 13, 16, 17, 19, 21, 23, 26 },
    { 2, 4, 6, 11, 12, 17, 18, 23, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 2, 3, 7, 10, 13, 16, 18, 23, 25 },
    { 4, 5, 7, 9, 12, 13, 15, 18, 20 },
    { 2, 3, 7, 11, 12, 19, 20, 21, 22 },
    { 4, 8, 9, 11, 17, 20, 22, 26, 27 },
    { 1, 3, 4, 12, 14, 16, 18, 22, 26 },
    { 2, 4, 6, 10, 13, 15, 19, 22, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 1, 5, 6, 9, 10, 17, 18, 25, 26 },
    { 3, 5, 10, 12, 15, 17, 22, 23, 27 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 4, 8, 10, 12, 18, 19, 21, 25, 27 },
    { 1, 3, 4, 11, 13, 15, 17, 21, 25 },
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 1, 3, 4, 9, 10, 19, 20, 23, 24 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 4, 5, 7, 10, 11, 14, 16, 17, 19 },
    { 2, 5, 8, 9, 14, 18, 19, 22, 23 },
    { 1, 2, 15, 18, 20, 21, 23, 26, 27 },
    { 1, 5, 6, 12, 14, 15, 19, 21, 24 },
    { 2, 5, 8, 10, 13, 17, 20, 21, 24 },
    { 2, 5, 8, 11, 12, 15, 16, 25, 26 },
    { 1, 7, 8, 12, 14, 17, 20, 23, 25 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 2, 3, 7, 9, 14, 15, 17, 24, 26 },
    { 1, 7, 8, 11, 13, 18, 19, 24, 26 }
];
/*
load "AD21-30.m";
Loading "AD21-30.m"
> od3:=od21;
> load "AD.m";
Loading "AD.m"
3-rank design= 13
weight distribution code= [ <0, 1>, <6, 126>, <9, 978>, <12, 45306>, <15,
357876>, <18, 768270>, <21, 391932>, <24, 29502>, <27, 332> ]
no of constant weight-9's 165
point group= Permutation group acting on a set of cardinality 27
Order = 36 = 2^2 * 3^2
    (1, 2, 6, 3, 5, 7)(4, 8, 27)(9, 26, 17)(11, 15)(12, 13, 19, 16, 21, 23)(14,
        22)(20, 24)
    (9, 10)(11, 13)(12, 14)(15, 21)(16, 22)(17, 25)(18, 26)(19, 24)(20, 23)
    (9, 17, 26)(10, 18, 25)(11, 20, 22)(12, 19, 21)(13, 16, 23)(14, 15, 24)
165
2-(27, 9, 4) Design with 39 blocks
*/
 //design no.22
 ablox:=
[
    { 10, 11, 14, 16, 17, 19, 22, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 15, 18, 20, 21, 23, 26 },
    { 3, 4, 6, 15, 18, 20, 22, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 5, 7, 8, 16, 17, 19, 21, 23, 26 },
    { 3, 4, 6, 10, 11, 14, 21, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 5, 7, 8, 9, 12, 13, 22, 24, 25 },
    { 3, 4, 6, 9, 12, 13, 16, 17, 19 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 5, 7, 8, 10, 11, 14, 15, 18, 20 },
    { 2, 6, 7, 11, 13, 19, 20, 23, 24 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 4, 8, 12, 14, 17, 18, 25, 26 },
    { 2, 6, 7, 9, 14, 15, 16, 25, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 4, 8, 10, 13, 19, 20, 21, 22 },
    { 2, 3, 7, 13, 14, 17, 18, 21, 22 },
    { 4, 5, 9, 11, 19, 20, 25, 26, 27 },
    { 1, 6, 8, 10, 12, 15, 16, 23, 24 },
    { 2, 5, 6, 10, 12, 17, 20, 22, 26 },
    { 3, 8, 13, 14, 15, 19, 23, 25, 27 },
    { 1, 4, 7, 9, 11, 16, 18, 21, 24 },
    { 2, 4, 5, 12, 14, 15, 19, 21, 24 },
    { 6, 8, 11, 13, 16, 18, 22, 26, 27 },
    { 1, 3, 7, 9, 10, 17, 20, 23, 25 },
    { 2, 4, 5, 10, 13, 16, 18, 23, 25 },
    { 6, 8, 9, 14, 17, 20, 21, 24, 27 },
    { 1, 3, 7, 11, 12, 15, 19, 22, 26 },
    { 2, 3, 8, 11, 12, 16, 20, 21, 25 },
    { 4, 7, 10, 13, 15, 17, 24, 26, 27 },
    { 1, 5, 6, 9, 14, 18, 19, 22, 23 },
    { 2, 3, 8, 9, 10, 18, 19, 24, 26 },
    { 4, 7, 12, 14, 16, 20, 22, 23, 27 },
    { 1, 5, 6, 11, 13, 15, 17, 21, 25 },
    { 2, 4, 8, 9, 11, 15, 17, 22, 23 },
    { 6, 7, 10, 12, 18, 19, 21, 25, 27 },
    { 1, 3, 5, 13, 14, 16, 20, 24, 26 }
];
 //aff geom design in code
 blos:=
[
    { 5, 7, 8, 10, 11, 14, 16, 17, 19 },
    { 1, 6, 7, 9, 14, 15, 19, 22, 26 },
    { 4, 8, 12, 14, 16, 18, 22, 26, 27 },
    { 1, 3, 8, 13, 14, 15, 16, 23, 24 },
    { 4, 8, 9, 11, 15, 19, 23, 25, 27 },
    { 2, 3, 5, 9, 10, 15, 19, 21, 24 },
    { 5, 7, 8, 9, 12, 13, 22, 24, 25 },
    { 5, 7, 8, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 16, 17, 19, 22, 24, 25, 27 },
    { 5, 6, 9, 14, 17, 18, 23, 24, 27 },
    { 3, 4, 6, 9, 10, 11, 12, 13, 14 },
    { 10, 11, 14, 21, 22, 23, 24, 25, 26 },
    { 5, 6, 11, 13, 15, 16, 21, 22, 27 },
    { 2, 6, 8, 11, 13, 18, 19, 24, 26 },
    { 3, 7, 9, 10, 16, 20, 22, 23, 27 },
    { 1, 3, 8, 9, 10, 17, 18, 25, 26 },
    { 3, 7, 11, 12, 15, 17, 24, 26, 27 },
    { 2, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 1, 6, 7, 11, 13, 17, 20, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 5, 6, 10, 12, 19, 20, 25, 26, 27 },
    { 3, 7, 13, 14, 18, 19, 21, 25, 27 },
    { 1, 4, 5, 10, 13, 18, 19, 22, 23 },
    { 2, 3, 5, 13, 14, 17, 20, 22, 26 },
    { 2, 3, 5, 11, 12, 16, 18, 23, 25 },
    { 1, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 1, 2, 10, 11, 14, 15, 18, 20, 27 },
    { 2, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 3, 4, 6, 15, 18, 20, 22, 24, 25 },
    { 1, 4, 5, 9, 11, 16, 20, 24, 26 },
    { 2, 4, 7, 10, 13, 15, 16, 25, 26 },
    { 3, 4, 6, 16, 17, 19, 21, 23, 26 },
    { 9, 12, 13, 15, 16, 17, 18, 19, 20 },
    { 1, 2, 9, 12, 13, 21, 23, 26, 27 },
    { 1, 6, 7, 10, 12, 16, 18, 21, 24 },
    { 1, 4, 5, 12, 14, 15, 17, 21, 25 },
    { 4, 8, 10, 13, 17, 20, 21, 24, 27 },
    { 2, 4, 7, 12, 14, 19, 20, 23, 24 },
    { 2, 4, 7, 9, 11, 17, 18, 21, 22 }
];
/* od3:=od22;
> load "AD.m";
Loading "AD.m"
3-rank design= 13
weight distribution code= [ <0, 1>, <6, 126>, <9, 978>, <12, 45306>, <15,
357876>, <18, 768270>, <21, 391932>, <24, 29502>, <27, 332> ]
no of constant weight-9's 165
point group= Permutation group acting on a set of cardinality 27
Order = 27 = 3^3
    (1, 15, 12)(2, 18, 13)(3, 22, 7)(4, 25, 5)(6, 24, 8)(9, 27, 20)(10, 16,
        23)(11, 19, 26)(14, 17, 21)
    (3, 6, 4)(5, 8, 7)(9, 13, 12)(10, 11, 14)(15, 18, 20)(21, 26, 23)
165
2-(27, 9, 4) Design with 39 blocks
*/ //design no. 23
 ablox:=
[
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 16, 17, 19, 21, 23, 26 },
    { 4, 5, 7, 15, 17, 20, 22, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 16, 18, 19, 21, 24, 25 },
    { 4, 5, 7, 9, 12, 14, 21, 24, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 10, 11, 13, 22, 23, 26 },
    { 4, 5, 7, 10, 11, 13, 16, 18, 19 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 9, 12, 14, 15, 17, 20 },
    { 2, 4, 6, 11, 14, 17, 19, 24, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 12, 13, 18, 20, 23, 25 },
    { 2, 4, 6, 9, 13, 16, 20, 22, 25 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 15, 19, 21, 26 },
    { 2, 4, 6, 10, 12, 15, 18, 21, 23 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 9, 11, 16, 17, 22, 24 },
    { 2, 3, 7, 12, 13, 15, 19, 22, 24 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 6, 11, 14, 16, 20, 21, 23 },
    { 2, 3, 7, 9, 11, 18, 20, 21, 26 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 5, 6, 10, 12, 17, 19, 22, 25 },
    { 2, 3, 7, 10, 14, 16, 17, 23, 25 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 5, 6, 9, 13, 15, 18, 24, 26 },
    { 2, 5, 8, 11, 13, 15, 17, 21, 25 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 1, 3, 4, 12, 14, 16, 18, 22, 26 },
    { 2, 5, 8, 9, 14, 18, 19, 22, 23 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 1, 3, 4, 10, 13, 17, 20, 21, 24 },
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 1, 3, 4, 9, 11, 15, 19, 23, 25 }
];
 //aff geom design in code
 blos:=
[
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 4, 5, 7, 9, 12, 14, 21, 24, 25 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 15, 19, 21, 26 },
    { 2, 4, 6, 9, 13, 16, 20, 22, 25 },
    { 4, 5, 7, 10, 11, 13, 16, 18, 19 },
    { 4, 5, 7, 15, 17, 20, 22, 23, 26 },
    { 2, 5, 8, 9, 13, 17, 19, 21, 23 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 2, 3, 7, 9, 13, 15, 18, 24, 26 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 3, 6, 8, 16, 18, 19, 21, 24, 25 },
    { 3, 6, 8, 9, 12, 14, 15, 17, 20 },
    { 1, 7, 8, 12, 13, 18, 20, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 2, 5, 8, 11, 14, 15, 18, 22, 25 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 10, 11, 13, 15, 17, 20, 21, 24, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 5, 6, 12, 13, 15, 19, 22, 24 },
    { 1, 5, 6, 10, 14, 16, 17, 23, 25 },
    { 2, 4, 6, 11, 14, 17, 19, 24, 26 },
    { 9, 12, 14, 16, 18, 19, 22, 23, 26 },
    { 3, 6, 8, 10, 11, 13, 22, 23, 26 },
    { 1, 5, 6, 9, 11, 18, 20, 21, 26 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 3, 4, 12, 13, 16, 17, 21, 26 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 2, 3, 7, 11, 14, 16, 20, 21, 23 },
    { 2, 4, 6, 10, 12, 15, 18, 21, 23 },
    { 2, 3, 7, 10, 12, 17, 19, 22, 25 },
    { 1, 7, 8, 9, 11, 16, 17, 22, 24 },
    { 1, 3, 4, 10, 14, 18, 20, 22, 24 },
    { 1, 3, 4, 9, 11, 15, 19, 23, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 }
];
/*> dc:=descode(27,blos,3);ac:=descode(27,ablox,3);
> Dim(ac),Dim(dc),Dim(ac meet dc);
12 10 10
> load "AD.m";
Loading "AD.m"
point group= Permutation group acting on a set of cardinality 27
Order = 24 = 2^3 * 3
    (1, 5)(2, 3)(4, 8)(9, 12, 23, 26, 19, 16)(10, 11, 24, 25, 20, 15)(13, 17, 
        21)(14, 18, 22)
    (1, 2)(3, 5)(4, 8)(6, 7)(9, 12)(10, 11)(15, 24)(16, 23)(17, 21)(18, 22)(19, 
        26)(20, 25)
    (9, 11)(10, 12)(13, 14)(15, 23)(16, 24)(17, 22)(18, 21)(19, 25)(20, 26)
    (9, 19, 23)(10, 20, 24)(11, 15, 25)(12, 16, 26)(13, 17, 21)(14, 18, 22)
75
2-(27, 9, 4) Design with 39 blocks
*/
> //design no. 24
 ablox:=
[
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 16, 17, 19, 21, 23, 26 },
    { 4, 5, 7, 16, 18, 19, 21, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 15, 17, 20, 22, 23, 26 },
    { 4, 5, 7, 10, 11, 13, 22, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 9, 12, 14, 21, 24, 25 },
    { 4, 5, 7, 9, 12, 14, 15, 17, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 11, 13, 16, 18, 19 },
    { 2, 4, 6, 11, 14, 17, 19, 24, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 12, 13, 18, 20, 23, 25 },
    { 2, 4, 6, 9, 13, 16, 20, 22, 25 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 15, 19, 21, 26 },
    { 2, 4, 6, 10, 12, 15, 18, 21, 23 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 9, 11, 16, 17, 22, 24 },
    { 2, 3, 7, 12, 13, 15, 19, 22, 24 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 6, 11, 14, 16, 20, 21, 23 },
    { 2, 3, 7, 9, 11, 18, 20, 21, 26 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 5, 6, 10, 12, 17, 19, 22, 25 },
    { 2, 3, 7, 10, 14, 16, 17, 23, 25 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 5, 6, 9, 13, 15, 18, 24, 26 },
    { 2, 5, 8, 11, 13, 15, 17, 21, 25 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 1, 3, 4, 12, 14, 16, 18, 22, 26 },
    { 2, 5, 8, 9, 14, 18, 19, 22, 23 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 1, 3, 4, 10, 13, 17, 20, 21, 24 },
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 1, 3, 4, 9, 11, 15, 19, 23, 25 }
];
 //aff geom design in code
 blos:=
[
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 4, 5, 7, 9, 12, 14, 21, 24, 25 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 15, 19, 21, 26 },
    { 2, 4, 6, 9, 13, 16, 20, 22, 25 },
    { 4, 5, 7, 10, 11, 13, 16, 18, 19 },
    { 4, 5, 7, 15, 17, 20, 22, 23, 26 },
    { 2, 5, 8, 9, 13, 17, 19, 21, 23 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 2, 3, 7, 9, 13, 15, 18, 24, 26 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 3, 6, 8, 16, 18, 19, 21, 24, 25 },
    { 3, 6, 8, 9, 12, 14, 15, 17, 20 },
    { 1, 7, 8, 12, 13, 18, 20, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 2, 5, 8, 11, 14, 15, 18, 22, 25 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 10, 11, 13, 15, 17, 20, 21, 24, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 5, 6, 12, 13, 15, 19, 22, 24 },
    { 1, 5, 6, 10, 14, 16, 17, 23, 25 },
    { 2, 4, 6, 11, 14, 17, 19, 24, 26 },
    { 9, 12, 14, 16, 18, 19, 22, 23, 26 },
    { 3, 6, 8, 10, 11, 13, 22, 23, 26 },
    { 1, 5, 6, 9, 11, 18, 20, 21, 26 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 3, 4, 12, 13, 16, 17, 21, 26 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 2, 3, 7, 11, 14, 16, 20, 21, 23 },
    { 2, 4, 6, 10, 12, 15, 18, 21, 23 },
    { 2, 3, 7, 10, 12, 17, 19, 22, 25 },
    { 1, 7, 8, 9, 11, 16, 17, 22, 24 },
    { 1, 3, 4, 10, 14, 18, 20, 22, 24 },
    { 1, 3, 4, 9, 11, 15, 19, 23, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 }
];
/*od3:=od24;
> load "AD.m";
Loading "AD.m"
3-rank design= 13
weight distribution code= [ <0, 1>, <6, 126>, <9, 978>, <12, 45306>, <15,
357876>, <18, 768270>, <21, 391932>, <24, 29502>, <27, 332> ]
no of constant weight-9's 165
point group= Permutation group acting on a set of cardinality 27
Order = 24 = 2^3 * 3
    (1, 8)(2, 4)(3, 5)(9, 26, 23, 16, 19, 12)(10, 25, 24, 15, 20, 11)(13, 17,
        21)(14, 18, 22)
    (1, 2)(3, 5)(4, 8)(6, 7)(9, 12)(10, 11)(15, 24)(16, 23)(17, 21)(18, 22)(19,
        26)(20, 25)
    (9, 11)(10, 12)(13, 14)(15, 23)(16, 24)(17, 22)(18, 21)(19, 25)(20, 26)
    (9, 19, 23)(10, 20, 24)(11, 15, 25)(12, 16, 26)(13, 17, 21)(14, 18, 22)
165
2-(27, 9, 4) Design with 39 blocks
*/
> //design no.25
> ablox;
[
    { 10, 12, 14, 15, 18, 19, 21, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 11, 13, 16, 17, 20, 22, 23, 26 },
    { 4, 5, 6, 16, 17, 19, 22, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 7, 8, 15, 18, 20, 21, 23, 26 },
    { 4, 5, 6, 10, 11, 14, 21, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 7, 8, 9, 12, 13, 22, 24, 25 },
    { 4, 5, 7, 9, 12, 14, 15, 17, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 11, 13, 16, 18, 19 },
    { 2, 4, 6, 12, 13, 18, 20, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 14, 17, 19, 24, 26 },
    { 2, 4, 7, 10, 13, 15, 19, 22, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 2, 4, 7, 9, 11, 16, 18, 21, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 2, 3, 6, 11, 14, 15, 20, 22, 24 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 7, 12, 13, 16, 19, 21, 23 },
    { 2, 3, 6, 9, 12, 17, 19, 21, 26 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 5, 7, 10, 11, 18, 20, 22, 25 },
    { 2, 3, 7, 10, 14, 16, 17, 23, 25 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 5, 6, 9, 13, 15, 18, 24, 26 },
    { 2, 5, 8, 11, 13, 15, 17, 21, 25 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 1, 3, 4, 12, 14, 16, 18, 22, 26 },
    { 2, 5, 8, 9, 14, 18, 19, 22, 23 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 1, 3, 4, 10, 13, 17, 20, 21, 24 },
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 1, 3, 4, 9, 11, 15, 19, 23, 25 }
]
> //aff geom design in code
> blos;
[
    { 4, 5, 6, 16, 17, 19, 22, 24, 25 },
    { 3, 7, 8, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 7, 8, 10, 11, 14, 16, 17, 19 },
    { 2, 4, 7, 10, 13, 15, 19, 22, 26 },
    { 4, 5, 6, 9, 12, 13, 15, 18, 20 },
    { 1, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 1, 5, 7, 10, 12, 18, 19, 21, 25 },
    { 2, 3, 6, 10, 13, 16, 18, 23, 25 },
    { 1, 6, 8, 11, 13, 18, 19, 24, 26 },
    { 1, 5, 7, 9, 14, 15, 17, 24, 26 },
    { 2, 4, 7, 12, 14, 17, 20, 23, 25 },
    { 4, 5, 6, 10, 11, 14, 21, 23, 26 },
    { 2, 3, 6, 12, 14, 15, 19, 21, 24 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 2, 3, 6, 9, 11, 17, 20, 22, 26 },
    { 2, 4, 7, 9, 11, 16, 18, 21, 24 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 9, 12, 13, 16, 17, 19, 21, 23, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 1, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 2, 5, 8, 9, 11, 15, 19, 23, 25 },
    { 1, 3, 4, 11, 13, 15, 17, 21, 25 },
    { 2, 5, 8, 12, 14, 16, 18, 22, 26 },
    { 1, 3, 4, 9, 14, 18, 19, 22, 23 },
    { 1, 5, 7, 11, 13, 16, 20, 22, 23 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 2, 5, 8, 10, 13, 17, 20, 21, 24 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 3, 4, 10, 12, 16, 20, 24, 26 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 3, 7, 8, 9, 12, 13, 22, 24, 25 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 }
];
/*
 load "AD21-30.m";
Loading "AD21-30.m"
> od3:=od25;
> load "AD.m";
Loading "AD.m"
3-rank design= 13
weight distribution code= [ <0, 1>, <6, 54>, <9, 1266>, <12, 45090>, <15,
357156>, <18, 770070>, <21, 390204>, <24, 30294>, <27, 188> ]
no of constant weight-9's 93
point group= Permutation group acting on a set of cardinality 27
Order = 24 = 2^3 * 3
    (1, 20, 18, 2, 19, 17)(3, 11, 13, 5, 12, 14)(4, 22, 6, 8, 21, 7)(9, 26, 24,
        10, 25, 23)(15, 16)
    (9, 15)(10, 16)(11, 19)(12, 20)(13, 18)(14, 17)(21, 22)(23, 25)(24, 26)
93
2-(27, 9, 4) Design with 39 blocks*/

 //design no. 26
 ablox:=
[
    { 10, 12, 13, 15, 18, 19, 22, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 11, 14, 16, 17, 20, 21, 23, 26 },
    { 4, 5, 7, 16, 17, 19, 21, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 15, 18, 20, 22, 23, 26 },
    { 4, 5, 7, 10, 11, 13, 22, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 9, 12, 14, 21, 24, 25 },
    { 4, 5, 7, 9, 12, 14, 15, 18, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 11, 13, 16, 17, 19 },
    { 2, 4, 6, 12, 13, 17, 20, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 14, 18, 19, 24, 26 },
    { 2, 4, 6, 10, 14, 15, 19, 21, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 9, 13, 16, 20, 22, 25 },
    { 2, 4, 6, 9, 11, 16, 18, 22, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 10, 12, 15, 17, 21, 23 },
    { 2, 3, 7, 11, 12, 19, 20, 21, 22 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 6, 13, 14, 15, 16, 23, 24 },
    { 2, 3, 7, 9, 13, 15, 17, 24, 26 },
    { 4, 8, 12, 14, 16, 19, 22, 23, 27 },
    { 1, 5, 6, 10, 11, 18, 20, 21, 25 },
    { 2, 3, 7, 10, 14, 16, 18, 23, 25 },
    { 4, 8, 11, 13, 15, 20, 21, 24, 27 },
    { 1, 5, 6, 9, 12, 17, 19, 22, 26 },
    { 2, 5, 8, 10, 12, 16, 20, 24, 26 },
    { 6, 7, 9, 11, 15, 19, 23, 25, 27 },
    { 1, 3, 4, 13, 14, 17, 18, 21, 22 },
    { 2, 5, 8, 9, 13, 18, 19, 21, 23 },
    { 6, 7, 10, 14, 17, 20, 22, 24, 27 },
    { 1, 3, 4, 11, 12, 15, 16, 25, 26 },
    { 2, 5, 8, 11, 14, 15, 17, 22, 25 },
    { 6, 7, 12, 13, 16, 18, 21, 26, 27 },
    { 1, 3, 4, 9, 10, 19, 20, 23, 24 }
];
 //aff geom design in code
 blos:=
[
    { 1, 5, 6, 13, 14, 15, 16, 23, 24 },
    { 2, 3, 7, 10, 14, 16, 18, 23, 25 },
    { 1, 2, 16, 17, 19, 21, 24, 25, 27 },
    { 2, 5, 8, 9, 13, 18, 19, 21, 23 },
    { 4, 5, 7, 9, 12, 14, 21, 24, 25 },
    { 4, 8, 11, 14, 16, 20, 21, 23, 27 },
    { 3, 6, 8, 9, 12, 14, 15, 18, 20 },
    { 4, 5, 7, 15, 16, 17, 18, 19, 20 },
    { 2, 3, 7, 11, 12, 19, 20, 21, 22 },
    { 1, 3, 4, 10, 12, 16, 20, 24, 26 },
    { 1, 7, 8, 13, 14, 19, 20, 25, 26 },
    { 2, 4, 6, 9, 13, 16, 20, 22, 25 },
    { 10, 11, 13, 15, 18, 20, 21, 24, 25 },
    { 6, 7, 11, 14, 15, 17, 22, 25, 27 },
    { 1, 3, 4, 13, 14, 17, 18, 21, 22 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 4, 5, 7, 10, 11, 13, 22, 23, 26 },
    { 3, 5, 12, 13, 17, 20, 23, 25, 27 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 3, 6, 8, 21, 22, 23, 24, 25, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 9, 11, 16, 18, 22, 24 },
    { 2, 3, 7, 9, 13, 15, 17, 24, 26 },
    { 2, 4, 6, 10, 14, 15, 19, 21, 26 },
    { 1, 7, 8, 10, 12, 15, 17, 21, 23 },
    { 4, 8, 12, 13, 15, 19, 22, 24, 27 },
    { 3, 5, 11, 14, 18, 19, 24, 26, 27 },
    { 1, 2, 15, 18, 20, 22, 23, 26, 27 },
    { 3, 6, 8, 10, 11, 13, 16, 17, 19 },
    { 2, 4, 6, 11, 12, 17, 18, 23, 24 },
    { 6, 7, 12, 13, 16, 18, 21, 26, 27 },
    { 2, 5, 8, 11, 12, 15, 16, 25, 26 },
    { 1, 3, 4, 9, 11, 15, 19, 23, 25 },
    { 1, 5, 6, 10, 12, 18, 19, 22, 25 },
    { 9, 12, 14, 16, 17, 19, 22, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 1, 5, 6, 9, 11, 17, 20, 21, 26 },
    { 2, 5, 8, 10, 14, 17, 20, 22, 24 }
];
/*od3:=od26;
> load "AD.m";
Loading "AD.m"
3-rank design= 13
weight distribution code= [ <0, 1>, <6, 126>, <9, 978>, <12, 45306>, <15,
357876>, <18, 768270>, <21, 391932>, <24, 29502>, <27, 332> ]
no of constant weight-9's 165
point group= Permutation group acting on a set of cardinality 27
Order = 18 = 2 * 3^2
    (1, 8, 5, 27, 6, 4)(2, 3, 7)(9, 23, 17, 14, 26, 16)(10, 15, 25, 13, 18,
        24)(11, 20, 21)(12, 22, 19)
    (9, 17, 26)(10, 18, 25)(11, 20, 21)(12, 19, 22)(13, 15, 24)(14, 16, 23)
165
2-(27, 9, 4) Design with 39 blocks
*/
> //design no. 27
> ablox;
[
    { 10, 12, 13, 15, 18, 20, 21, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 11, 14, 16, 17, 19, 22, 24, 26 },
    { 3, 4, 7, 16, 18, 19, 21, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 5, 6, 8, 15, 17, 20, 22, 23, 26 },
    { 4, 5, 7, 11, 13, 14, 21, 22, 23 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 9, 10, 12, 24, 25, 26 },
    { 5, 6, 7, 9, 10, 11, 18, 19, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 4, 8, 12, 13, 14, 15, 16, 17 },
    { 2, 4, 6, 12, 14, 18, 19, 23, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 13, 17, 20, 24, 25 },
    { 2, 4, 6, 9, 13, 16, 20, 22, 25 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 15, 19, 21, 26 },
    { 2, 4, 6, 10, 11, 15, 17, 21, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 9, 12, 16, 18, 22, 23 },
    { 2, 3, 7, 10, 13, 17, 18, 22, 26 },
    { 4, 8, 9, 11, 15, 19, 23, 25, 27 },
    { 1, 5, 6, 12, 14, 16, 20, 21, 24 },
    { 2, 5, 7, 11, 12, 15, 16, 25, 26 },
    { 4, 8, 10, 14, 18, 20, 22, 24, 27 },
    { 1, 3, 6, 9, 13, 17, 19, 21, 23 },
    { 2, 3, 7, 9, 14, 15, 20, 23, 24 },
    { 6, 8, 11, 13, 16, 18, 21, 26, 27 },
    { 1, 4, 5, 10, 12, 17, 19, 22, 25 },
    { 2, 5, 8, 10, 13, 16, 19, 23, 24 },
    { 4, 7, 9, 12, 17, 20, 21, 26, 27 },
    { 1, 3, 6, 11, 14, 15, 18, 22, 25 },
    { 2, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 6, 7, 10, 14, 16, 17, 23, 25, 27 },
    { 1, 4, 5, 9, 13, 15, 18, 24, 26 },
    { 2, 5, 8, 9, 14, 17, 18, 21, 25 },
    { 6, 7, 12, 13, 15, 19, 22, 24, 27 },
    { 1, 3, 4, 10, 11, 16, 20, 23, 26 }
]
> //aff geom design in code
> blos;
[
    { 2, 7, 9, 20, 21, 23, 24, 26, 27 },
    { 1, 2, 5, 14, 16, 17, 18, 20, 21 },
    { 1, 3, 4, 10, 11, 16, 20, 23, 26 },
    { 2, 3, 8, 13, 14, 15, 16, 23, 24 },
    { 1, 6, 12, 15, 16, 19, 20, 24, 27 },
    { 4, 8, 9, 11, 15, 19, 23, 25, 27 },
    { 4, 8, 10, 14, 18, 20, 22, 24, 27 },
    { 5, 6, 8, 10, 11, 13, 16, 18, 19 },
    { 3, 5, 9, 12, 16, 18, 22, 23, 27 },
    { 5, 6, 8, 15, 17, 20, 22, 23, 26 },
    { 4, 5, 7, 11, 13, 14, 21, 22, 23 },
    { 1, 7, 8, 11, 14, 17, 19, 24, 26 },
    { 2, 4, 6, 10, 13, 15, 20, 21, 25 },
    { 3, 6, 7, 9, 11, 14, 15, 18, 20 },
    { 1, 6, 9, 10, 13, 14, 17, 23, 27 },
    { 2, 3, 8, 9, 10, 17, 18, 25, 26 },
    { 1, 7, 8, 10, 12, 15, 18, 21, 23 },
    { 1, 3, 4, 12, 14, 15, 17, 22, 25 },
    { 1, 2, 5, 10, 19, 22, 23, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 2, 7, 10, 11, 12, 14, 16, 25, 27 },
    { 3, 6, 7, 10, 12, 13, 22, 24, 26 },
    { 3, 5, 11, 13, 17, 20, 24, 25, 27 },
    { 9, 10, 11, 15, 16, 17, 21, 22, 24 },
    { 2, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 3, 6, 7, 16, 17, 19, 21, 23, 25 },
    { 12, 13, 14, 18, 19, 20, 23, 25, 26 },
    { 2, 7, 13, 15, 17, 18, 19, 22, 27 },
    { 2, 4, 6, 9, 14, 16, 19, 22, 26 },
    { 4, 5, 7, 9, 10, 12, 17, 19, 20 },
    { 4, 5, 7, 15, 16, 18, 24, 25, 26 },
    { 2, 4, 6, 11, 12, 17, 18, 23, 24 },
    { 1, 6, 11, 18, 21, 22, 25, 26, 27 },
    { 1, 7, 8, 9, 13, 16, 20, 22, 25 },
    { 1, 2, 5, 9, 11, 12, 13, 15, 26 },
    { 4, 8, 12, 13, 16, 17, 21, 26, 27 },
    { 1, 3, 4, 9, 13, 18, 19, 21, 24 },
    { 3, 5, 10, 14, 15, 19, 21, 26, 27 },
    { 5, 6, 8, 9, 12, 14, 21, 24, 25 }
];
/*load "AD21-30.m";
Loading "AD21-30.m"
> od3:=od27;
> load "AD.m";
Loading "AD.m"
3-rank design= 13
weight distribution code= [ <0, 1>, <6, 126>, <9, 978>, <12, 45306>, <15,
357876>, <18, 768270>, <21, 391932>, <24, 29502>, <27, 332> ]
no of constant weight-9's 165
point group= Permutation group acting on a set of cardinality 27
Order = 18 = 2 * 3^2
    (1, 12, 27, 20, 2, 21)(3, 25, 6, 10, 7, 18)(4, 15, 8, 23, 5, 13)(9, 17, 19,
        22, 24, 14)(11, 26, 16)
    (3, 5)(4, 6)(7, 8)(9, 13)(10, 14)(11, 12)(15, 19)(16, 20)(17, 18)(21,
        26)(22, 25)(23, 24)
165
2-(27, 9, 4) Design with 39 blocks
*/
> //design no. 28
> ablox;
[
    { 10, 11, 14, 16, 17, 19, 21, 23, 26 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 15, 18, 20, 22, 24, 25 },
    { 3, 4, 6, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 5, 7, 8, 16, 17, 19, 22, 24, 25 },
    { 3, 4, 6, 10, 11, 14, 22, 24, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 5, 7, 8, 9, 12, 13, 21, 23, 26 },
    { 3, 4, 6, 9, 12, 13, 16, 17, 19 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 5, 7, 8, 10, 11, 14, 15, 18, 20 },
    { 2, 6, 8, 11, 13, 18, 19, 24, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 4, 7, 12, 14, 17, 20, 23, 25 },
    { 2, 4, 8, 10, 13, 16, 20, 21, 25 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 6, 7, 9, 14, 15, 19, 22, 26 },
    { 2, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 4, 5, 9, 11, 19, 20, 25, 26, 27 },
    { 1, 3, 7, 13, 14, 16, 18, 21, 24 },
    { 2, 4, 7, 9, 11, 17, 18, 21, 22 },
    { 3, 8, 13, 14, 15, 19, 23, 25, 27 },
    { 1, 5, 6, 10, 12, 16, 20, 24, 26 },
    { 2, 3, 7, 9, 10, 19, 20, 23, 24 },
    { 4, 8, 12, 14, 16, 18, 22, 26, 27 },
    { 1, 5, 6, 11, 13, 15, 17, 21, 25 },
    { 2, 3, 7, 11, 12, 15, 16, 25, 26 },
    { 6, 8, 9, 14, 17, 20, 21, 24, 27 },
    { 1, 4, 5, 10, 13, 18, 19, 22, 23 },
    { 2, 5, 6, 9, 14, 16, 18, 23, 25 },
    { 4, 7, 10, 13, 15, 17, 24, 26, 27 },
    { 1, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 2, 3, 5, 13, 14, 17, 20, 22, 26 },
    { 6, 7, 10, 12, 18, 19, 21, 25, 27 },
    { 1, 4, 8, 9, 11, 15, 16, 23, 24 },
    { 2, 4, 5, 12, 14, 15, 19, 21, 24 },
    { 6, 7, 11, 13, 16, 20, 22, 23, 27 },
    { 1, 3, 8, 9, 10, 17, 18, 25, 26 }
]
> //aff geom design in code
> blos;
[
    { 5, 7, 8, 10, 11, 14, 16, 17, 19 },
    { 1, 6, 7, 9, 14, 15, 19, 22, 26 },
    { 4, 8, 12, 14, 16, 18, 22, 26, 27 },
    { 1, 3, 8, 13, 14, 15, 16, 23, 24 },
    { 4, 8, 9, 11, 15, 19, 23, 25, 27 },
    { 2, 3, 5, 9, 10, 15, 19, 21, 24 },
    { 5, 7, 8, 9, 12, 13, 22, 24, 25 },
    { 5, 7, 8, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 16, 17, 19, 22, 24, 25, 27 },
    { 5, 6, 9, 14, 17, 18, 23, 24, 27 },
    { 3, 4, 6, 9, 10, 11, 12, 13, 14 },
    { 10, 11, 14, 21, 22, 23, 24, 25, 26 },
    { 5, 6, 11, 13, 15, 16, 21, 22, 27 },
    { 2, 6, 8, 11, 13, 18, 19, 24, 26 },
    { 3, 7, 9, 10, 16, 20, 22, 23, 27 },
    { 1, 3, 8, 9, 10, 17, 18, 25, 26 },
    { 3, 7, 11, 12, 15, 17, 24, 26, 27 },
    { 2, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 1, 6, 7, 11, 13, 17, 20, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 5, 6, 10, 12, 19, 20, 25, 26, 27 },
    { 3, 7, 13, 14, 18, 19, 21, 25, 27 },
    { 1, 4, 5, 10, 13, 18, 19, 22, 23 },
    { 2, 3, 5, 13, 14, 17, 20, 22, 26 },
    { 2, 3, 5, 11, 12, 16, 18, 23, 25 },
    { 1, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 1, 2, 10, 11, 14, 15, 18, 20, 27 },
    { 2, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 3, 4, 6, 15, 18, 20, 22, 24, 25 },
    { 1, 4, 5, 9, 11, 16, 20, 24, 26 },
    { 2, 4, 7, 10, 13, 15, 16, 25, 26 },
    { 3, 4, 6, 16, 17, 19, 21, 23, 26 },
    { 9, 12, 13, 15, 16, 17, 18, 19, 20 },
    { 1, 2, 9, 12, 13, 21, 23, 26, 27 },
    { 1, 6, 7, 10, 12, 16, 18, 21, 24 },
    { 1, 4, 5, 12, 14, 15, 17, 21, 25 },
    { 4, 8, 10, 13, 17, 20, 21, 24, 27 },
    { 2, 4, 7, 12, 14, 19, 20, 23, 24 },
    { 2, 4, 7, 9, 11, 17, 18, 21, 22 }
];

/*
load "AD21-30.m";
Loading "AD21-30.m"
> od3:=od28;
> load "AD.m";
Loading "AD.m"
3-rank design= 13
weight distribution code= [ <0, 1>, <6, 126>, <9, 978>, <12, 45306>, <15,
357876>, <18, 768270>, <21, 391932>, <24, 29502>, <27, 332> ]
no of constant weight-9's 165
point group= Permutation group acting on a set of cardinality 27
Order = 18 = 2 * 3^2
    (1, 22, 17, 27, 25, 16)(2, 24, 19)(3, 13, 10, 6, 9, 11)(4, 12, 14)(5, 15,
        21)(7, 18, 23, 8, 20, 26)
    (2, 27)(3, 6)(5, 8)(9, 13)(10, 11)(15, 18)(16, 19)(21, 26)(22, 24)
165
2-(27, 9, 4) Design with 39 blocks
*/> dc:=descode(27,blos,3);ac:=descode(27,ablox,3);
> Dim(ac),Dim(dc),Dim(ac meet dc);
12 10 10
> 
> //design no.29
> ablox;
[
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 16, 17, 19, 21, 23, 26 },
    { 4, 5, 6, 16, 17, 19, 22, 24, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 7, 8, 15, 18, 20, 21, 23, 26 },
    { 4, 5, 6, 10, 11, 14, 21, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 7, 8, 9, 12, 13, 22, 24, 25 },
    { 4, 5, 7, 9, 12, 14, 15, 17, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 11, 13, 16, 18, 19 },
    { 2, 4, 6, 12, 13, 18, 20, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 14, 17, 19, 24, 26 },
    { 2, 4, 7, 10, 13, 15, 19, 22, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 2, 4, 7, 9, 11, 16, 18, 21, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 2, 3, 6, 12, 14, 15, 19, 21, 24 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 7, 11, 13, 16, 20, 22, 23 },
    { 2, 3, 6, 9, 11, 17, 20, 22, 26 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 5, 7, 10, 12, 18, 19, 21, 25 },
    { 2, 3, 7, 10, 14, 16, 17, 23, 25 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 1, 5, 6, 9, 13, 15, 18, 24, 26 },
    { 2, 5, 8, 11, 12, 15, 16, 25, 26 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 1, 3, 4, 13, 14, 17, 18, 21, 22 },
    { 2, 5, 8, 9, 14, 18, 19, 22, 23 },
    { 6, 7, 11, 13, 15, 17, 21, 25, 27 },
    { 1, 3, 4, 10, 12, 16, 20, 24, 26 },
    { 2, 5, 8, 10, 13, 17, 20, 21, 24 },
    { 6, 7, 12, 14, 16, 18, 22, 26, 27 },
    { 1, 3, 4, 9, 11, 15, 19, 23, 25 }
]
> //aff geom design in code
> blos;
[
    { 4, 5, 6, 16, 17, 19, 22, 24, 25 },
    { 3, 7, 8, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 7, 8, 10, 11, 14, 16, 17, 19 },
    { 2, 4, 7, 10, 13, 15, 19, 22, 26 },
    { 4, 5, 6, 9, 12, 13, 15, 18, 20 },
    { 1, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 1, 5, 7, 10, 12, 18, 19, 21, 25 },
    { 2, 3, 6, 10, 13, 16, 18, 23, 25 },
    { 1, 6, 8, 11, 13, 18, 19, 24, 26 },
    { 1, 5, 7, 9, 14, 15, 17, 24, 26 },
    { 2, 4, 7, 12, 14, 17, 20, 23, 25 },
    { 4, 5, 6, 10, 11, 14, 21, 23, 26 },
    { 2, 3, 6, 12, 14, 15, 19, 21, 24 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 6, 7, 11, 12, 15, 16, 25, 26, 27 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 2, 3, 6, 9, 11, 17, 20, 22, 26 },
    { 2, 4, 7, 9, 11, 16, 18, 21, 24 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 9, 12, 13, 16, 17, 19, 21, 23, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 4, 8, 11, 12, 19, 20, 21, 22, 27 },
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 1, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 2, 5, 8, 9, 11, 15, 19, 23, 25 },
    { 1, 3, 4, 11, 13, 15, 17, 21, 25 },
    { 2, 5, 8, 12, 14, 16, 18, 22, 26 },
    { 1, 3, 4, 9, 14, 18, 19, 22, 23 },
    { 1, 5, 7, 11, 13, 16, 20, 22, 23 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 2, 5, 8, 10, 13, 17, 20, 21, 24 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 3, 4, 10, 12, 16, 20, 24, 26 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 3, 7, 8, 9, 12, 13, 22, 24, 25 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 }
]
/*
load "AD21-30.m";
Loading "AD21-30.m"
> od3:=od29;
> load "AD.m";
Loading "AD.m"
3-rank design= 12
weight distribution code= [ <0, 1>, <6, 36>, <9, 366>, <12, 14904>, <15,
119808>, <18, 255360>, <21, 131220>, <24, 9594>, <27, 152> ]
no of constant weight-9's 75
point group= Permutation group acting on a set of cardinality 27
Order = 12 = 2^2 * 3
    (1, 12)(2, 19)(3, 16)(4, 26)(5, 9)(6, 17)(7, 13)(8, 23)(11, 25)(14, 18)(20,
        24)(21, 27)
    (3, 4)(5, 8)(6, 7)(9, 19)(10, 20)(11, 15)(12, 16)(13, 17)(14, 18)
75
2-(27, 9, 4) Design with 39 blocks*/