//design no. 50
 ablox:=
[
    { 10, 11, 14, 15, 18, 20, 21, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 16, 17, 19, 22, 23, 26 },
    { 4, 5, 7, 16, 17, 20, 21, 23, 25 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 15, 18, 19, 22, 24, 26 },
    { 4, 5, 7, 9, 11, 14, 22, 24, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 10, 12, 13, 21, 23, 25 },
    { 4, 5, 7, 10, 12, 13, 15, 18, 19 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 9, 11, 14, 16, 17, 20 },
    { 2, 4, 6, 12, 14, 17, 19, 24, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 13, 18, 20, 23, 26 },
    { 2, 4, 6, 9, 13, 15, 20, 21, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 16, 19, 22, 25 },
    { 2, 4, 6, 10, 11, 16, 18, 22, 23 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 9, 12, 15, 17, 21, 24 },
    { 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, 16, 18, 24, 25 },
    { 4, 8, 12, 14, 15, 20, 22, 23, 27 },
    { 1, 5, 6, 10, 11, 17, 19, 21, 26 },
    { 2, 3, 7, 10, 14, 15, 17, 23, 26 },
    { 4, 8, 11, 13, 16, 19, 21, 24, 27 },
    { 1, 5, 6, 9, 12, 18, 20, 22, 25 },
    { 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, 21, 23 },
    { 6, 7, 10, 13, 17, 20, 22, 24, 27 },
    { 1, 3, 4, 11, 12, 15, 16, 25, 26 },
    { 2, 5, 8, 11, 13, 15, 17, 22, 25 },
    { 6, 7, 12, 14, 16, 18, 21, 26, 27 },
    { 1, 3, 4, 9, 10, 19, 20, 23, 24 }
];
 //aff geom design in code
 blos:=
[
    { 1, 3, 4, 11, 12, 15, 16, 25, 26 },
    { 2, 4, 6, 12, 14, 17, 19, 24, 25 },
    { 2, 3, 7, 11, 13, 16, 19, 21, 24 },
    { 1, 5, 6, 9, 13, 16, 18, 24, 25 },
    { 1, 5, 6, 10, 14, 15, 17, 23, 26 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 4, 5, 7, 15, 16, 17, 18, 19, 20 },
    { 3, 5, 10, 11, 16, 18, 22, 23, 27 },
    { 2, 4, 6, 9, 10, 15, 16, 21, 22 },
    { 1, 7, 8, 9, 13, 15, 20, 21, 26 },
    { 1, 2, 16, 17, 20, 21, 23, 25, 27 },
    { 4, 8, 9, 12, 18, 20, 22, 25, 27 },
    { 2, 4, 6, 11, 13, 18, 20, 23, 26 },
    { 9, 11, 14, 15, 18, 19, 21, 23, 25 },
    { 1, 7, 8, 11, 12, 17, 18, 23, 24 },
    { 3, 6, 8, 9, 11, 14, 16, 17, 20 },
    { 6, 7, 9, 12, 16, 19, 23, 26, 27 },
    { 2, 5, 8, 11, 13, 15, 17, 22, 25 },
    { 3, 5, 9, 12, 15, 17, 21, 24, 27 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 1, 2, 15, 18, 19, 22, 24, 26, 27 },
    { 6, 7, 10, 11, 15, 20, 24, 25, 27 },
    { 3, 6, 8, 21, 22, 23, 24, 25, 26 },
    { 2, 5, 8, 12, 14, 16, 18, 21, 26 },
    { 1, 5, 6, 11, 12, 19, 20, 21, 22 },
    { 3, 6, 8, 10, 12, 13, 15, 18, 19 },
    { 1, 3, 4, 9, 13, 17, 19, 22, 23 },
    { 4, 8, 10, 11, 17, 19, 21, 26, 27 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 4, 5, 7, 9, 11, 14, 22, 24, 26 },
    { 4, 5, 7, 10, 12, 13, 21, 23, 25 },
    { 1, 3, 4, 10, 14, 18, 20, 21, 24 },
    { 1, 7, 8, 10, 14, 16, 19, 22, 25 },
    { 2, 3, 7, 12, 14, 15, 20, 22, 23 },
    { 10, 12, 13, 16, 17, 20, 22, 24, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 2, 5, 8, 9, 10, 19, 20, 23, 24 },
    { 2, 3, 7, 9, 10, 17, 18, 25, 26 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 }
];
/*
load "AD41-50.m";
Loading "AD41-50.m"
> od3:=od50;
> 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 = 6 = 2 * 3
    (1, 4)(5, 8)(6, 27)(10, 20)(11, 15)(12, 26)(14, 21)(17, 22)(19, 23)
    (2, 8)(3, 4)(7, 27)(10, 24)(11, 15)(13, 17)(14, 21)(16, 26)(19, 23)
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);
13 10 10
*/
 //design no.51
 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, 16, 17, 19, 21, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 5, 7, 8, 15, 18, 20, 22, 24, 25 },
    { 3, 4, 6, 9, 12, 13, 22, 24, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 5, 7, 8, 10, 11, 14, 21, 23, 26 },
    { 3, 4, 6, 10, 11, 14, 15, 18, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 5, 7, 8, 9, 12, 13, 16, 17, 19 },
    { 2, 6, 8, 11, 13, 17, 18, 25, 26 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 4, 7, 12, 14, 19, 20, 23, 24 },
    { 2, 6, 7, 9, 14, 15, 19, 22, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 4, 8, 10, 13, 16, 20, 21, 25 },
    { 2, 3, 7, 13, 14, 16, 18, 21, 24 },
    { 4, 5, 9, 11, 19, 20, 25, 26, 27 },
    { 1, 6, 8, 10, 12, 15, 17, 22, 23 },
    { 2, 5, 6, 10, 12, 16, 20, 24, 26 },
    { 3, 8, 13, 14, 15, 19, 23, 25, 27 },
    { 1, 4, 7, 9, 11, 17, 18, 21, 22 },
    { 2, 3, 7, 9, 10, 17, 20, 23, 25 },
    { 4, 8, 12, 14, 16, 18, 22, 26, 27 },
    { 1, 5, 6, 11, 13, 15, 19, 21, 24 },
    { 2, 4, 5, 10, 13, 18, 19, 22, 23 },
    { 6, 8, 9, 14, 17, 20, 21, 24, 27 },
    { 1, 3, 7, 11, 12, 15, 16, 25, 26 },
    { 2, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 4, 7, 10, 13, 15, 17, 24, 26, 27 },
    { 1, 5, 6, 9, 14, 16, 18, 23, 25 },
    { 2, 4, 8, 9, 11, 15, 16, 23, 24 },
    { 6, 7, 10, 12, 18, 19, 21, 25, 27 },
    { 1, 3, 5, 13, 14, 17, 20, 22, 26 },
    { 2, 4, 5, 12, 14, 15, 17, 21, 25 },
    { 6, 7, 11, 13, 16, 20, 22, 23, 27 },
    { 1, 3, 8, 9, 10, 18, 19, 24, 26 }
];
 //aff geom design in code
 blos:=
[
    { 1, 4, 7, 12, 14, 19, 20, 23, 24 },
    { 3, 4, 5, 6, 7, 8, 16, 17, 19 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 2, 5, 7, 8, 9, 12, 13, 27 },
    { 5, 7, 8, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 16, 17, 19, 22, 24, 25, 27 },
    { 1, 2, 3, 4, 6, 21, 23, 26, 27 },
    { 3, 8, 13, 14, 15, 19, 23, 25, 27 },
    { 3, 4, 6, 9, 10, 11, 12, 13, 14 },
    { 3, 7, 9, 10, 16, 20, 22, 23, 27 },
    { 2, 3, 7, 13, 14, 16, 18, 21, 24 },
    { 2, 4, 8, 12, 14, 17, 18, 25, 26 },
    { 4, 7, 9, 11, 18, 19, 21, 25, 27 },
    { 2, 6, 7, 11, 13, 17, 20, 23, 25 },
    { 6, 7, 9, 14, 15, 17, 24, 26, 27 },
    { 5, 7, 8, 10, 11, 14, 22, 24, 25 },
    { 5, 6, 10, 12, 19, 20, 25, 26, 27 },
    { 1, 4, 5, 10, 13, 16, 18, 23, 25 },
    { 2, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 1, 3, 8, 9, 10, 18, 19, 24, 26 },
    { 2, 6, 8, 10, 12, 15, 16, 23, 24 },
    { 1, 2, 10, 11, 14, 15, 18, 20, 27 },
    { 1, 3, 5, 13, 14, 17, 20, 22, 26 },
    { 4, 5, 12, 14, 15, 16, 21, 22, 27 },
    { 1, 6, 7, 10, 12, 17, 18, 21, 22 },
    { 2, 4, 5, 9, 11, 16, 20, 24, 26 },
    { 3, 4, 6, 15, 18, 20, 22, 24, 25 },
    { 1, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 6, 8, 11, 13, 16, 18, 22, 26, 27 },
    { 1, 4, 8, 9, 11, 15, 17, 22, 23 },
    { 2, 5, 6, 9, 14, 18, 19, 22, 23 },
    { 2, 4, 7, 10, 13, 15, 19, 22, 26 },
    { 10, 11, 14, 16, 17, 19, 21, 23, 26 },
    { 1, 3, 7, 11, 12, 15, 16, 25, 26 },
    { 2, 3, 5, 9, 10, 15, 17, 21, 25 },
    { 9, 12, 13, 15, 16, 17, 18, 19, 20 },
    { 1, 5, 6, 11, 13, 15, 19, 21, 24 },
    { 9, 12, 13, 21, 22, 23, 24, 25, 26 },
    { 4, 8, 10, 13, 17, 20, 21, 24, 27 }
];
/*> dc:=descode(27,blos,3);ac:=descode(27,ablox,3); 
> Dim(ac),Dim(dc),Dim(ac meet dc);
13 10 10
> quit;
load "AD51-60.m";
Loading "AD51-60.m"
> od3:=od51;
> 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
165
2-(27, 9, 4) Design with 39 blocks
*/
 //design no.52
 ablox:=
[
    { 10, 11, 14, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 16, 17, 19, 22, 24, 25 },
    { 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, 9, 12, 13, 21, 23, 26 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 5, 7, 8, 10, 11, 14, 22, 24, 25 },
    { 3, 4, 6, 10, 11, 14, 16, 17, 19 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 5, 7, 8, 9, 12, 13, 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, 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, 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, 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, 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 },
    { 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 }
];
/*
> dc:=descode(27,blos,3);ac:=descode(27,ablox,3); 
> Dim(ac),Dim(dc),Dim(ac meet dc);
13 10 10
> au:=PointGroup(ades);
> au;
Permutation group au acting on a set of cardinality 27
Order = 6 = 2 * 3
    (1, 2)(3, 6)(5, 7)(9, 13)(10, 11)(15, 20)(17, 19)(21, 23)(24, 25)
    (2, 27)(4, 6)(5, 7)(11, 14)(12, 13)(15, 20)(16, 19)(21, 23)(22, 24)

load "AD51-60.m";
Loading "AD51-60.m"
> od3:=od52;
> 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
165
2-(27, 9, 4) Design with 39 blocks
*/ //design No.53
 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, 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, 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, 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, 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, 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 },
    { 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:=
[
    { 6, 7, 10, 12, 18, 19, 21, 25, 27 },
    { 1, 6, 7, 9, 14, 15, 19, 22, 26 },
    { 3, 4, 5, 6, 7, 8, 16, 17, 19 },
    { 3, 8, 11, 12, 17, 20, 21, 24, 27 },
    { 4, 8, 9, 11, 15, 19, 23, 25, 27 },
    { 2, 5, 6, 10, 12, 17, 20, 22, 26 },
    { 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 },
    { 4, 7, 10, 13, 15, 17, 24, 26, 27 },
    { 3, 4, 6, 21, 22, 23, 24, 25, 26 },
    { 1, 3, 8, 9, 10, 17, 18, 25, 26 },
    { 3, 7, 9, 10, 16, 20, 22, 23, 27 },
    { 1, 3, 7, 13, 14, 16, 18, 21, 24 },
    { 1, 2, 5, 7, 8, 10, 11, 14, 27 },
    { 2, 4, 5, 10, 13, 16, 18, 23, 25 },
    { 1, 4, 8, 10, 13, 19, 20, 21, 22 },
    { 4, 5, 12, 14, 15, 16, 21, 22, 27 },
    { 1, 6, 8, 10, 12, 15, 16, 23, 24 },
    { 2, 4, 8, 12, 14, 18, 19, 24, 26 },
    { 1, 5, 6, 11, 13, 15, 17, 21, 25 },
    { 1, 2, 3, 4, 6, 15, 18, 20, 27 },
    { 2, 6, 7, 11, 13, 19, 20, 23, 24 },
    { 1, 3, 5, 11, 12, 18, 19, 22, 23 },
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 2, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 1, 4, 5, 9, 11, 16, 20, 24, 26 },
    { 6, 8, 11, 13, 16, 18, 22, 26, 27 },
    { 1, 4, 7, 12, 14, 17, 20, 23, 25 },
    { 10, 11, 14, 16, 17, 19, 21, 23, 26 },
    { 2, 3, 7, 11, 12, 15, 16, 25, 26 },
    { 2, 3, 8, 13, 14, 15, 17, 22, 23 },
    { 9, 12, 13, 15, 16, 17, 18, 19, 20 },
    { 1, 2, 9, 12, 13, 21, 23, 26, 27 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 2, 4, 7, 9, 11, 17, 18, 21, 22 }
];
/*
> dc:=descode(27,blos,3);ac:=descode(27,ablox,3); 
> Dim(ac),Dim(dc),Dim(ac meet dc);
13 10 10
> au:=AutomorphismGroup(ades);
> au;
Permutation group au acting on a set of cardinality 27
Order = 6 = 2 * 3
    (1, 2)(3, 6)(5, 7)(9, 13)(10, 11)(15, 20)(17, 19)(21, 23)(24, 25)
    (2, 27)(4, 6)(5, 7)(11, 14)(12, 13)(15, 20)(16, 19)(21, 23)(22, 24)

load "AD51-60.m";
Loading "AD51-60.m"
> od3:=od53;
> 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
165
2-(27, 9, 4) Design with 39 blocks*/ //design no.54
 ablox:=
[
    { 10, 11, 14, 15, 18, 20, 21, 23, 26 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 16, 17, 19, 22, 24, 25 },
    { 3, 4, 6, 16, 17, 19, 21, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 5, 7, 8, 15, 18, 20, 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, 15, 18, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 5, 7, 8, 10, 11, 14, 16, 17, 19 },
    { 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, 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, 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, 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, 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 },
    { 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:=
[
    { 6, 7, 10, 12, 18, 19, 21, 25, 27 },
    { 1, 6, 7, 9, 14, 15, 19, 22, 26 },
    { 3, 4, 5, 6, 7, 8, 16, 17, 19 },
    { 3, 8, 11, 12, 17, 20, 21, 24, 27 },
    { 4, 8, 9, 11, 15, 19, 23, 25, 27 },
    { 2, 5, 6, 10, 12, 17, 20, 22, 26 },
    { 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 },
    { 4, 7, 10, 13, 15, 17, 24, 26, 27 },
    { 3, 4, 6, 21, 22, 23, 24, 25, 26 },
    { 1, 3, 8, 9, 10, 17, 18, 25, 26 },
    { 3, 7, 9, 10, 16, 20, 22, 23, 27 },
    { 1, 3, 7, 13, 14, 16, 18, 21, 24 },
    { 1, 2, 5, 7, 8, 10, 11, 14, 27 },
    { 2, 4, 5, 10, 13, 16, 18, 23, 25 },
    { 1, 4, 8, 10, 13, 19, 20, 21, 22 },
    { 4, 5, 12, 14, 15, 16, 21, 22, 27 },
    { 1, 6, 8, 10, 12, 15, 16, 23, 24 },
    { 2, 4, 8, 12, 14, 18, 19, 24, 26 },
    { 1, 5, 6, 11, 13, 15, 17, 21, 25 },
    { 1, 2, 3, 4, 6, 15, 18, 20, 27 },
    { 2, 6, 7, 11, 13, 19, 20, 23, 24 },
    { 1, 3, 5, 11, 12, 18, 19, 22, 23 },
    { 10, 11, 14, 15, 18, 20, 22, 24, 25 },
    { 2, 6, 8, 9, 14, 16, 20, 21, 25 },
    { 1, 4, 5, 9, 11, 16, 20, 24, 26 },
    { 6, 8, 11, 13, 16, 18, 22, 26, 27 },
    { 1, 4, 7, 12, 14, 17, 20, 23, 25 },
    { 10, 11, 14, 16, 17, 19, 21, 23, 26 },
    { 2, 3, 7, 11, 12, 15, 16, 25, 26 },
    { 2, 3, 8, 13, 14, 15, 17, 22, 23 },
    { 9, 12, 13, 15, 16, 17, 18, 19, 20 },
    { 1, 2, 9, 12, 13, 21, 23, 26, 27 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 2, 4, 7, 9, 11, 17, 18, 21, 22 }
];
/*
> dc:=descode(27,blos,3);ac:=descode(27,ablox,3); 
> Dim(ac),Dim(dc),Dim(ac meet dc);
13 10 10
> AutomorphismGroup(ades);
Permutation group acting on a set of cardinality 27
Order = 6 = 2 * 3
    (1, 2)(3, 6)(5, 7)(9, 13)(10, 11)(15, 20)(17, 19)(21, 23)(24, 25)
    (2, 27)(4, 6)(5, 7)(11, 14)(12, 13)(15, 20)(16, 19)(21, 23)(22, 24)

 load "AD51-60.m";
Loading "AD51-60.m"
> od3:=od54;
> 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
165
2-(27, 9, 4) Design with 39 blocks
*/ //design no. 55
 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, 16, 17, 19, 21, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 5, 7, 8, 15, 18, 20, 22, 24, 25 },
    { 3, 4, 6, 9, 12, 13, 22, 24, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 5, 7, 8, 10, 11, 14, 21, 23, 26 },
    { 3, 4, 6, 10, 11, 14, 15, 18, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 5, 7, 8, 9, 12, 13, 16, 17, 19 },
    { 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 "AD51-60.m";
Loading "AD51-60.m"
> od3:=od55;
> 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 = 6 = 2 * 3
    (1, 2)(3, 6)(5, 7)(9, 13)(10, 11)(15, 20)(17, 19)(21, 23)(24, 25)
    (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*/
 //design no.56
 ablox:=
[
    { 10, 11, 13, 15, 17, 20, 21, 24, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 14, 16, 18, 19, 22, 23, 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, 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, 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 "AD51-60.m";
Loading "AD51-60.m"
> od3:=od56;
> 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 = 6 = 2 * 3
    (1, 22, 25)(2, 12, 11)(3, 26, 10)(4, 18, 24)(5, 14, 21)(6, 23, 17)(7, 9,
        20)(8, 16, 13)(15, 27, 19)
    (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. 57
 ablox:=
[
    { 11, 12, 13, 15, 16, 18, 21, 25, 26 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 10, 14, 17, 19, 20, 22, 23, 24 },
    { 3, 4, 6, 15, 18, 20, 22, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 5, 7, 8, 16, 17, 19, 21, 24, 25 },
    { 3, 4, 6, 10, 11, 14, 21, 24, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 5, 7, 8, 9, 12, 13, 22, 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, 7, 11, 13, 17, 20, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 4, 8, 12, 14, 18, 19, 24, 26 },
    { 2, 6, 7, 9, 14, 15, 19, 21, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 4, 8, 10, 13, 16, 20, 22, 25 },
    { 2, 3, 7, 13, 14, 16, 18, 22, 24 },
    { 4, 5, 9, 11, 19, 20, 25, 26, 27 },
    { 1, 6, 8, 10, 12, 15, 17, 21, 23 },
    { 2, 5, 6, 10, 12, 16, 20, 24, 26 },
    { 3, 8, 13, 14, 15, 19, 23, 25, 27 },
    { 1, 4, 7, 9, 11, 17, 18, 21, 22 },
    { 2, 4, 5, 10, 13, 18, 19, 21, 23 },
    { 6, 8, 11, 14, 16, 17, 22, 26, 27 },
    { 1, 3, 7, 9, 12, 15, 20, 24, 25 },
    { 2, 4, 5, 12, 14, 15, 17, 22, 25 },
    { 6, 8, 9, 13, 18, 20, 21, 24, 27 },
    { 1, 3, 7, 10, 11, 16, 19, 23, 26 },
    { 2, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 4, 7, 10, 13, 15, 17, 24, 26, 27 },
    { 1, 5, 6, 9, 14, 16, 18, 23, 25 },
    { 2, 3, 8, 9, 10, 17, 18, 25, 26 },
    { 4, 7, 12, 14, 16, 20, 21, 23, 27 },
    { 1, 5, 6, 11, 13, 15, 19, 22, 24 },
    { 2, 4, 8, 9, 11, 15, 16, 23, 24 },
    { 6, 7, 10, 12, 18, 19, 22, 25, 27 },
    { 1, 3, 5, 13, 14, 17, 20, 21, 26 }
];
//aff geom design in code
 blos:=
[
    { 1, 5, 6, 11, 13, 15, 19, 22, 24 },
    { 1, 5, 6, 10, 12, 17, 20, 21, 26 },
    { 2, 4, 5, 12, 14, 15, 17, 22, 25 },
    { 1, 2, 16, 17, 19, 21, 24, 25, 27 },
    { 2, 3, 8, 13, 14, 15, 16, 23, 24 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 3, 7, 13, 14, 17, 18, 21, 22 },
    { 9, 12, 13, 15, 18, 20, 21, 24, 25 },
    { 3, 4, 6, 15, 16, 17, 18, 19, 20 },
    { 3, 4, 6, 9, 10, 11, 12, 13, 14 },
    { 4, 7, 10, 13, 15, 17, 24, 26, 27 },
    { 6, 8, 9, 14, 17, 20, 22, 24, 27 },
    { 3, 4, 6, 21, 22, 23, 24, 25, 26 },
    { 5, 7, 8, 15, 18, 20, 22, 23, 26 },
    { 4, 7, 12, 14, 16, 20, 21, 23, 27 },
    { 2, 3, 8, 9, 10, 17, 18, 25, 26 },
    { 5, 7, 8, 10, 11, 14, 21, 24, 25 },
    { 2, 6, 7, 11, 13, 17, 20, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 2, 4, 5, 10, 13, 18, 19, 21, 23 },
    { 4, 7, 9, 11, 18, 19, 22, 25, 27 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 2, 3, 8, 11, 12, 19, 20, 21, 22 },
    { 1, 4, 8, 10, 13, 16, 20, 22, 25 },
    { 6, 8, 11, 13, 16, 18, 21, 26, 27 },
    { 1, 2, 10, 11, 14, 15, 18, 20, 27 },
    { 1, 4, 8, 9, 11, 15, 17, 21, 23 },
    { 1, 4, 8, 12, 14, 18, 19, 24, 26 },
    { 2, 4, 5, 9, 11, 16, 20, 24, 26 },
    { 5, 7, 8, 9, 12, 13, 16, 17, 19 },
    { 1, 5, 6, 9, 14, 16, 18, 23, 25 },
    { 6, 8, 10, 12, 15, 19, 23, 25, 27 },
    { 1, 3, 7, 11, 12, 15, 16, 25, 26 },
    { 2, 6, 7, 9, 14, 15, 19, 21, 26 },
    { 10, 11, 14, 16, 17, 19, 22, 23, 26 },
    { 1, 3, 7, 9, 10, 19, 20, 23, 24 },
    { 2, 6, 7, 10, 12, 16, 18, 22, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 2, 9, 12, 13, 22, 23, 26, 27 }
];
/*

od3:=od57;
> 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
93
2-(27, 9, 4) Design with 39 blocks*/ //design no. 58
 ablox:=
[
    { 10, 11, 14, 16, 18, 20, 21, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 15, 17, 19, 22, 24, 26 },
    { 4, 5, 7, 16, 18, 19, 22, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 15, 17, 20, 21, 24, 25 },
    { 4, 5, 7, 10, 12, 13, 21, 24, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 9, 11, 14, 22, 23, 26 },
    { 4, 5, 7, 9, 11, 14, 15, 17, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 12, 13, 16, 18, 19 },
    { 2, 4, 6, 12, 14, 17, 19, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 13, 18, 20, 24, 26 },
    { 2, 4, 6, 9, 13, 16, 20, 21, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 15, 19, 22, 25 },
    { 2, 4, 6, 10, 11, 15, 18, 22, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 9, 12, 16, 17, 21, 23 },
    { 2, 3, 7, 13, 14, 15, 16, 23, 24 },
    { 4, 8, 9, 10, 17, 18, 25, 26, 27 },
    { 1, 5, 6, 11, 12, 19, 20, 21, 22 },
    { 2, 3, 7, 10, 11, 17, 19, 21, 26 },
    { 4, 8, 12, 14, 16, 20, 22, 24, 27 },
    { 1, 5, 6, 9, 13, 15, 18, 23, 25 },
    { 2, 3, 7, 9, 12, 18, 20, 22, 25 },
    { 4, 8, 11, 13, 15, 19, 21, 23, 27 },
    { 1, 5, 6, 10, 14, 16, 17, 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, 21, 24 },
    { 6, 7, 11, 13, 16, 17, 22, 25, 27 },
    { 1, 3, 4, 10, 12, 15, 20, 23, 26 },
    { 2, 5, 8, 10, 13, 17, 20, 22, 23 },
    { 6, 7, 12, 14, 15, 18, 21, 26, 27 },
    { 1, 3, 4, 9, 11, 16, 19, 24, 25 }
];
 //aff geom design in code
 blos:=
[
    { 2, 3, 7, 12, 14, 16, 20, 22, 24 },
    { 1, 7, 8, 12, 14, 17, 19, 23, 25 },
    { 2, 4, 6, 10, 11, 15, 18, 22, 24 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 2, 5, 8, 9, 13, 17, 19, 22, 24 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 1, 3, 4, 9, 12, 15, 19, 24, 26 },
    { 4, 5, 7, 9, 10, 11, 12, 13, 14 },
    { 1, 2, 9, 11, 14, 15, 17, 20, 27 },
    { 1, 3, 4, 13, 14, 17, 18, 21, 22 },
    { 3, 6, 8, 9, 11, 14, 22, 23, 26 },
    { 1, 5, 6, 10, 14, 16, 17, 24, 26 },
    { 4, 8, 9, 12, 18, 20, 22, 25, 27 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 3, 6, 8, 15, 16, 17, 18, 19, 20 },
    { 6, 7, 9, 10, 19, 20, 23, 24, 27 },
    { 1, 2, 10, 12, 13, 16, 18, 19, 27 },
    { 1, 5, 6, 11, 12, 19, 20, 21, 22 },
    { 6, 7, 11, 13, 16, 17, 22, 25, 27 },
    { 3, 5, 9, 13, 16, 20, 21, 26, 27 },
    { 6, 7, 12, 14, 15, 18, 21, 26, 27 },
    { 9, 11, 14, 16, 18, 19, 21, 24, 25 },
    { 10, 12, 13, 15, 17, 20, 22, 23, 26 },
    { 1, 7, 8, 11, 13, 18, 20, 24, 26 },
    { 4, 5, 7, 16, 18, 19, 22, 23, 26 },
    { 3, 6, 8, 10, 12, 13, 21, 24, 25 },
    { 4, 8, 10, 11, 17, 19, 21, 26, 27 },
    { 2, 4, 6, 13, 14, 19, 20, 25, 26 },
    { 4, 5, 7, 15, 17, 20, 21, 24, 25 },
    { 1, 7, 8, 9, 10, 15, 16, 21, 22 },
    { 2, 5, 8, 11, 12, 15, 16, 25, 26 },
    { 2, 5, 8, 10, 14, 18, 20, 21, 23 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 2, 3, 7, 9, 10, 17, 18, 25, 26 },
    { 2, 3, 7, 11, 13, 15, 19, 21, 23 },
    { 1, 5, 6, 9, 13, 15, 18, 23, 25 },
    { 1, 3, 4, 10, 11, 16, 20, 23, 25 },
    { 3, 5, 10, 14, 15, 19, 22, 25, 27 },
    { 2, 4, 6, 9, 12, 16, 17, 21, 23 }
];
/*

load "AD51-60.m";
Loading "AD51-60.m"
> od3:=od58;
> 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 = 4 = 2^2
    (1, 5)(2, 3)(4, 8)(9, 10)(11, 22)(12, 21)(13, 16)(14, 15)(17, 25)(18,
        26)(19, 20)(23, 24)
    (1, 2)(3, 5)(4, 8)(6, 7)(11, 14)(12, 13)(15, 22)(16, 21)(17, 26)(18, 25)(19,
        24)(20, 23)
165
2-(27, 9, 4) Design with 39 blocks
*/
 //design no. 59
 ablox:=
[
    { 10, 11, 14, 16, 18, 20, 21, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 9, 12, 13, 15, 17, 19, 22, 24, 26 },
    { 4, 5, 7, 16, 18, 19, 22, 23, 26 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 3, 6, 8, 15, 17, 20, 21, 24, 25 },
    { 4, 5, 7, 10, 12, 13, 21, 24, 25 },
    { 1, 2, 15, 16, 17, 18, 19, 20, 27 },
    { 3, 6, 8, 9, 11, 14, 22, 23, 26 },
    { 4, 5, 7, 9, 11, 14, 15, 17, 20 },
    { 1, 2, 21, 22, 23, 24, 25, 26, 27 },
    { 3, 6, 8, 10, 12, 13, 16, 18, 19 },
    { 2, 4, 6, 12, 14, 17, 19, 23, 25 },
    { 3, 5, 9, 10, 15, 16, 21, 22, 27 },
    { 1, 7, 8, 11, 13, 18, 20, 24, 26 },
    { 2, 4, 6, 9, 13, 16, 20, 21, 26 },
    { 3, 5, 11, 12, 17, 18, 23, 24, 27 },
    { 1, 7, 8, 10, 14, 15, 19, 22, 25 },
    { 2, 4, 6, 10, 11, 15, 18, 22, 24 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 },
    { 1, 7, 8, 9, 12, 16, 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, 18, 23, 25 },
    { 4, 8, 12, 14, 16, 20, 22, 24, 27 },
    { 1, 5, 6, 10, 11, 17, 19, 21, 26 },
    { 2, 3, 7, 10, 14, 16, 17, 24, 26 },
    { 4, 8, 11, 13, 15, 19, 21, 23, 27 },
    { 1, 5, 6, 9, 12, 18, 20, 22, 25 },
    { 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, 21, 24 },
    { 6, 7, 11, 13, 16, 17, 22, 25, 27 },
    { 1, 3, 4, 10, 12, 15, 20, 23, 26 },
    { 2, 5, 8, 10, 13, 17, 20, 22, 23 },
    { 6, 7, 12, 14, 15, 18, 21, 26, 27 },
    { 1, 3, 4, 9, 11, 16, 19, 24, 25 }
];
 //aff geom design in code
 blos:=
[
    { 2, 3, 7, 12, 14, 16, 20, 22, 24 },
    { 1, 3, 4, 11, 12, 15, 16, 25, 26 },
    { 2, 4, 6, 11, 13, 18, 20, 24, 26 },
    { 4, 5, 7, 9, 11, 14, 22, 23, 26 },
    { 3, 6, 8, 10, 12, 13, 16, 18, 19 },
    { 1, 3, 4, 10, 14, 18, 20, 21, 23 },
    { 4, 8, 13, 14, 15, 16, 23, 24, 27 },
    { 4, 5, 7, 15, 16, 17, 18, 19, 20 },
    { 2, 4, 6, 9, 10, 15, 16, 21, 22 },
    { 1, 7, 8, 10, 14, 15, 19, 22, 25 },
    { 1, 3, 4, 9, 13, 17, 19, 22, 24 },
    { 3, 5, 9, 12, 16, 17, 21, 23, 27 },
    { 1, 2, 16, 18, 19, 22, 23, 26, 27 },
    { 6, 7, 10, 11, 16, 20, 23, 25, 27 },
    { 1, 5, 6, 10, 14, 16, 17, 24, 26 },
    { 4, 8, 9, 12, 18, 20, 22, 25, 27 },
    { 3, 5, 10, 11, 15, 18, 22, 24, 27 },
    { 1, 7, 8, 11, 12, 17, 18, 23, 24 },
    { 4, 5, 7, 10, 12, 13, 21, 24, 25 },
    { 2, 4, 6, 12, 14, 17, 19, 23, 25 },
    { 1, 2, 3, 4, 5, 6, 7, 8, 27 },
    { 1, 2, 15, 17, 20, 21, 24, 25, 27 },
    { 3, 6, 8, 21, 22, 23, 24, 25, 26 },
    { 1, 5, 6, 11, 12, 19, 20, 21, 22 },
    { 6, 7, 9, 12, 15, 19, 24, 26, 27 },
    { 9, 11, 14, 16, 18, 19, 21, 24, 25 },
    { 10, 12, 13, 15, 17, 20, 22, 23, 26 },
    { 4, 8, 10, 11, 17, 19, 21, 26, 27 },
    { 6, 7, 13, 14, 17, 18, 21, 22, 27 },
    { 1, 7, 8, 9, 13, 16, 20, 21, 26 },
    { 3, 6, 8, 9, 11, 14, 15, 17, 20 },
    { 1, 2, 9, 10, 11, 12, 13, 14, 27 },
    { 2, 5, 8, 9, 10, 19, 20, 23, 24 },
    { 2, 3, 7, 9, 10, 17, 18, 25, 26 },
    { 2, 3, 7, 11, 13, 15, 19, 21, 23 },
    { 1, 5, 6, 9, 13, 15, 18, 23, 25 },
    { 2, 5, 8, 11, 13, 16, 17, 22, 25 },
    { 2, 5, 8, 12, 14, 15, 18, 21, 26 },
    { 3, 5, 13, 14, 19, 20, 25, 26, 27 }
];



/* load "AD51-60.m";
Loading "AD51-60.m"
> od3:=od59;
> 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 = 4 = 2^2
    (1, 5)(2, 3)(4, 8)(9, 10)(11, 22)(12, 21)(13, 16)(14, 15)(17, 25)(18,
        26)(19, 20)(23, 24)
    (1, 2)(3, 5)(4, 8)(6, 7)(11, 14)(12, 13)(15, 22)(16, 21)(17, 26)(18, 25)(19,
        24)(20, 23)
165
2-(27, 9, 4) Design with 39 blocks*/