From fleming@math.clemson.edu Tue Mar 30 08:40:15 1999 //design No.40 of Lam and Tonchev lamton40 //the blocks of the affine geometry design in the code of No.40 > blos; [ { 4, 7, 8, 9, 10, 13, 22, 25, 26 }, { 1, 8, 9, 16, 17, 18, 20, 25, 27 }, { 4, 5, 7, 16, 18, 19, 21, 24, 25 }, { 1, 2, 6, 9, 10, 11, 12, 17, 22 }, { 1, 3, 4, 10, 12, 16, 20, 24, 26 }, { 3, 8, 13, 14, 15, 20, 23, 26, 27 }, { 4, 5, 6, 9, 12, 13, 15, 18, 20 }, { 3, 5, 6, 17, 19, 20, 22, 25, 26 }, { 2, 3, 7, 9, 11, 18, 20, 21, 26 }, { 1, 6, 8, 11, 13, 18, 19, 24, 26 }, { 3, 6, 8, 9, 12, 14, 21, 24, 25 }, { 3, 7, 8, 10, 11, 14, 16, 17, 19 }, { 2, 3, 6, 10, 13, 16, 18, 23, 25 }, { 1, 7, 8, 10, 12, 15, 18, 21, 23 }, { 6, 7, 9, 12, 16, 19, 23, 26, 27 }, { 1, 3, 4, 6, 7, 11, 15, 25, 27 }, { 4, 6, 8, 15, 16, 17, 22, 23, 24 }, { 2, 5, 6, 7, 8, 10, 20, 24, 27 }, { 2, 5, 8, 12, 13, 16, 17, 21, 26 }, { 1, 3, 4, 9, 13, 17, 19, 21, 23 }, { 10, 11, 13, 15, 17, 20, 21, 24, 25 }, { 2, 3, 12, 15, 17, 18, 19, 24, 27 }, { 1, 5, 7, 9, 14, 15, 17, 24, 26 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 2, 7, 13, 15, 16, 19, 20, 22 }, { 11, 12, 14, 15, 16, 18, 22, 25, 26 }, { 2, 4, 6, 10, 14, 15, 19, 21, 26 }, { 4, 5, 10, 11, 17, 18, 23, 26, 27 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 2, 3, 4, 5, 8, 14, 18, 22 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 2, 5, 8, 9, 11, 15, 19, 23, 25 }, { 9, 10, 14, 18, 19, 20, 22, 23, 24 }, { 2, 4, 7, 12, 14, 17, 20, 23, 25 }, { 3, 5, 7, 11, 12, 13, 22, 23, 24 }, { 1, 5, 10, 12, 13, 14, 19, 25, 27 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 2, 4, 9, 11, 13, 14, 16, 24, 27 }, { 1, 5, 6, 11, 14, 16, 20, 21, 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, 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, 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, 6, 9, 11, 16, 17, 22, 24 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 7, 8, 10, 12, 15, 18, 21, 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, 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, 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 } ] > //corected design no. 41 > 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, 6, 9, 11, 14, 16, 17, 20 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 7, 8, 10, 12, 13, 15, 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, 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, 7, 9, 12, 15, 17, 22, 24 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 6, 8, 10, 11, 16, 18, 21, 23 }, { 2, 3, 6, 11, 13, 16, 19, 22, 24 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 7, 12, 14, 15, 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, 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; [ { 3, 8, 10, 13, 18, 19, 25, 26, 27 }, { 9, 10, 12, 16, 19, 20, 23, 24, 26 }, { 1, 6, 8, 9, 13, 15, 20, 22, 26 }, { 4, 5, 7, 16, 18, 19, 21, 24, 25 }, { 3, 5, 6, 15, 17, 18, 23, 24, 26 }, { 2, 4, 13, 15, 16, 18, 20, 23, 27 }, { 2, 5, 6, 7, 8, 9, 19, 23, 27 }, { 4, 5, 9, 14, 17, 20, 25, 26, 27 }, { 2, 3, 7, 9, 11, 18, 20, 21, 26 }, { 3, 6, 8, 9, 12, 14, 21, 24, 25 }, { 3, 7, 8, 16, 17, 20, 22, 23, 25 }, { 2, 3, 10, 11, 12, 14, 17, 23, 27 }, { 6, 7, 11, 12, 15, 16, 25, 26, 27 }, { 1, 7, 8, 10, 12, 15, 18, 21, 23 }, { 9, 11, 14, 15, 18, 19, 22, 23, 25 }, { 1, 2, 6, 12, 17, 18, 19, 20, 25 }, { 2, 5, 8, 12, 13, 16, 17, 21, 26 }, { 4, 5, 6, 10, 12, 13, 22, 23, 25 }, { 1, 3, 4, 9, 13, 17, 19, 21, 23 }, { 10, 11, 13, 15, 17, 20, 21, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 2, 4, 7, 9, 12, 15, 17, 22, 24 }, { 4, 7, 8, 11, 13, 14, 23, 24, 26 }, { 1, 5, 9, 11, 12, 13, 18, 24, 27 }, { 2, 4, 6, 10, 14, 15, 19, 21, 26 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 3, 4, 6, 7, 10, 20, 24, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 1, 2, 7, 9, 10, 13, 14, 16, 25 }, { 1, 8, 14, 15, 16, 17, 19, 24, 27 }, { 1, 3, 4, 12, 14, 16, 18, 22, 26 }, { 3, 5, 7, 12, 13, 14, 15, 19, 20 }, { 4, 6, 8, 9, 10, 11, 16, 17, 18 }, { 1, 2, 3, 4, 5, 8, 11, 15, 25 }, { 2, 3, 6, 11, 13, 16, 19, 22, 24 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 1, 5, 6, 11, 14, 16, 20, 21, 23 }, { 1, 5, 7, 10, 11, 17, 19, 22, 26 } ] > WD(d41n); [ <0, 1>, <6, 8>, <9, 2>, <12, 160>, <13, 110>, <15, 496>, <16, 1244>, <18, 9886>, <19, 21062>, <21, 46552>, <22, 185432>, <24, 160228>, <25, 396950>, <27, 212202>, <28, 338468>, <30, 95416>, <31, 111512>, <33, 6182>, <34, 7886>, <36, 308>, <37, 218> ] > WD(c41n); [ <0, 1>, <6, 126>, <9, 978>, <12, 45306>, <15, 357876>, <18, 768270>, <21, 391932>, <24, 29502>, <27, 332> ] > load "AD41-50.m"; Loading "AD41-50.m" > od3:=od42; > 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, 3)(2, 5)(6, 7)(9, 23)(10, 24)(13, 17)(14, 18)(15, 25)(16, 26) (3, 4)(5, 8)(6, 7)(15, 25)(16, 26)(17, 21)(18, 22)(19, 23)(20, 24) 165 2-(27, 9, 4) Design with 39 blocks > c42:=C; > IsEquivalent(c42,c41n); true Mapping from: ModTupFld: V to ModTupFld: V > quit; Total time: 35.700 seconds From fleming@math.clemson.edu Tue Mar 30 08:31:06 1999 Date: Mon, 29 Mar 1999 10:17:24 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton42 lamton42 > blos; [ { 3, 8, 10, 13, 18, 19, 25, 26, 27 }, { 9, 10, 12, 16, 19, 20, 23, 24, 26 }, { 1, 6, 8, 9, 13, 15, 20, 22, 26 }, { 4, 5, 7, 16, 18, 19, 21, 24, 25 }, { 3, 5, 6, 15, 17, 18, 23, 24, 26 }, { 2, 4, 13, 15, 16, 18, 20, 23, 27 }, { 2, 5, 6, 7, 8, 9, 19, 23, 27 }, { 4, 5, 9, 14, 17, 20, 25, 26, 27 }, { 2, 3, 7, 9, 11, 18, 20, 21, 26 }, { 3, 6, 8, 9, 12, 14, 21, 24, 25 }, { 3, 7, 8, 16, 17, 20, 22, 23, 25 }, { 2, 3, 10, 11, 12, 14, 17, 23, 27 }, { 6, 7, 11, 12, 15, 16, 25, 26, 27 }, { 1, 7, 8, 10, 12, 15, 18, 21, 23 }, { 9, 11, 14, 15, 18, 19, 22, 23, 25 }, { 1, 2, 6, 12, 17, 18, 19, 20, 25 }, { 2, 5, 8, 12, 13, 16, 17, 21, 26 }, { 4, 5, 6, 10, 12, 13, 22, 23, 25 }, { 1, 3, 4, 9, 13, 17, 19, 21, 23 }, { 10, 11, 13, 15, 17, 20, 21, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 2, 4, 7, 9, 12, 15, 17, 22, 24 }, { 4, 7, 8, 11, 13, 14, 23, 24, 26 }, { 1, 5, 9, 11, 12, 13, 18, 24, 27 }, { 2, 4, 6, 10, 14, 15, 19, 21, 26 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 3, 4, 6, 7, 10, 20, 24, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 1, 2, 7, 9, 10, 13, 14, 16, 25 }, { 1, 8, 14, 15, 16, 17, 19, 24, 27 }, { 1, 3, 4, 12, 14, 16, 18, 22, 26 }, { 3, 5, 7, 12, 13, 14, 15, 19, 20 }, { 4, 6, 8, 9, 10, 11, 16, 17, 18 }, { 1, 2, 3, 4, 5, 8, 11, 15, 25 }, { 2, 3, 6, 11, 13, 16, 19, 22, 24 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 1, 5, 6, 11, 14, 16, 20, 21, 23 }, { 1, 5, 7, 10, 11, 17, 19, 22, 26 } ] > 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, 6, 10, 12, 13, 22, 23, 25 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 3, 7, 8, 9, 11, 14, 21, 24, 26 }, { 4, 5, 6, 9, 11, 14, 16, 17, 20 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 7, 8, 10, 12, 13, 15, 18, 19 }, { 2, 4, 7, 11, 13, 18, 20, 23, 26 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 6, 8, 12, 14, 17, 19, 24, 25 }, { 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, 7, 9, 12, 15, 17, 22, 24 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 6, 8, 10, 11, 16, 18, 21, 23 }, { 2, 3, 6, 11, 13, 16, 19, 22, 24 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 7, 12, 14, 15, 20, 21, 23 }, { 2, 3, 6, 9, 12, 18, 20, 21, 25 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 1, 5, 7, 10, 11, 17, 19, 22, 26 }, { 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 } ] From fleming@math.clemson.edu Tue Mar 30 08:30:51 1999 Date: Mon, 29 Mar 1999 10:18:18 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton43 lamton43 > 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 } ] > ablox; [ { 10, 11, 12, 15, 16, 20, 23, 25, 26 }, { 1, 2, 3, 4, 5, 6, 7, 8, 27 }, { 9, 13, 14, 17, 18, 19, 21, 22, 24 }, { 4, 5, 7, 15, 17, 20, 21, 24, 25 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 6, 8, 16, 18, 19, 22, 23, 26 }, { 4, 5, 7, 9, 11, 14, 22, 23, 26 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 3, 6, 8, 10, 12, 13, 21, 24, 25 }, { 4, 5, 7, 10, 12, 13, 16, 18, 19 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 6, 8, 9, 11, 14, 15, 17, 20 }, { 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, 14, 16, 18, 21, 25 }, { 6, 7, 9, 10, 19, 20, 23, 24, 27 }, { 1, 3, 4, 12, 13, 15, 17, 22, 26 }, { 2, 5, 8, 9, 12, 15, 19, 24, 26 }, { 6, 7, 11, 13, 16, 17, 22, 25, 27 }, { 1, 3, 4, 10, 14, 18, 20, 21, 23 }, { 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 } ] //design no. 44 ablox:= [ { 10, 11, 12, 18, 19, 20, 21, 22, 25 }, { 1, 2, 3, 4, 5, 6, 7, 8, 27 }, { 9, 13, 14, 15, 16, 17, 23, 24, 26 }, { 4, 5, 7, 15, 18, 19, 22, 24, 26 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 6, 8, 16, 17, 20, 21, 23, 25 }, { 4, 5, 7, 9, 12, 14, 21, 23, 25 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 3, 6, 8, 10, 11, 13, 22, 24, 26 }, { 4, 5, 7, 10, 11, 13, 16, 17, 20 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 6, 8, 9, 12, 14, 15, 18, 19 }, { 2, 4, 6, 11, 14, 18, 20, 23, 26 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 7, 8, 12, 13, 17, 19, 24, 25 }, { 2, 4, 6, 9, 13, 16, 19, 22, 25 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 1, 7, 8, 10, 14, 15, 20, 21, 26 }, { 2, 4, 6, 10, 12, 15, 17, 21, 24 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 7, 8, 9, 11, 16, 18, 22, 23 }, { 2, 3, 7, 12, 13, 15, 20, 22, 23 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 6, 11, 14, 16, 19, 21, 24 }, { 2, 3, 7, 9, 11, 17, 19, 21, 26 }, { 4, 8, 12, 14, 16, 20, 22, 24, 27 }, { 1, 5, 6, 10, 13, 15, 18, 23, 25 }, { 2, 3, 7, 10, 14, 16, 18, 24, 25 }, { 4, 8, 11, 13, 15, 19, 21, 23, 27 }, { 1, 5, 6, 9, 12, 17, 20, 22, 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, 13, 18, 20, 21, 24 }, { 6, 7, 11, 14, 15, 17, 22, 25, 27 }, { 1, 3, 4, 10, 12, 16, 19, 23, 26 }, { 2, 5, 8, 10, 14, 17, 19, 22, 23 }, { 6, 7, 12, 13, 16, 18, 21, 26, 27 }, { 1, 3, 4, 9, 11, 15, 20, 24, 25 } ]; //aff geom design in the code blos:= [ { 1, 5, 6, 10, 14, 16, 18, 24, 25 }, { 4, 5, 7, 10, 11, 13, 22, 24, 26 }, { 3, 6, 8, 15, 18, 19, 22, 24, 26 }, { 3, 5, 10, 12, 15, 17, 21, 24, 27 }, { 1, 2, 10, 11, 13, 16, 17, 20, 27 }, { 4, 5, 7, 15, 16, 17, 18, 19, 20 }, { 1, 7, 8, 11, 14, 18, 20, 23, 26 }, { 2, 5, 8, 12, 13, 16, 18, 21, 26 }, { 1, 5, 6, 9, 13, 15, 17, 23, 26 }, { 6, 7, 9, 13, 18, 20, 21, 24, 27 }, { 1, 3, 4, 13, 14, 17, 18, 21, 22 }, { 2, 4, 6, 9, 13, 16, 19, 22, 25 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 6, 7, 11, 12, 15, 16, 25, 26, 27 }, { 1, 7, 8, 12, 13, 17, 19, 24, 25 }, { 4, 5, 7, 9, 12, 14, 21, 23, 25 }, { 1, 2, 3, 4, 5, 6, 7, 8, 27 }, { 3, 6, 8, 9, 10, 11, 12, 13, 14 }, { 1, 3, 4, 9, 11, 15, 20, 24, 25 }, { 9, 12, 14, 16, 17, 20, 22, 24, 26 }, { 2, 3, 7, 10, 12, 18, 20, 22, 25 }, { 1, 5, 6, 11, 12, 19, 20, 21, 22 }, { 2, 4, 6, 10, 14, 15, 20, 21, 26 }, { 3, 5, 9, 11, 16, 18, 22, 23, 27 }, { 1, 3, 4, 10, 12, 16, 19, 23, 26 }, { 1, 2, 9, 12, 14, 15, 18, 19, 27 }, { 2, 3, 7, 9, 11, 17, 19, 21, 26 }, { 10, 11, 13, 15, 18, 19, 21, 23, 25 }, { 2, 5, 8, 11, 14, 15, 17, 22, 25 }, { 2, 3, 7, 13, 14, 15, 16, 23, 24 }, { 2, 4, 6, 11, 12, 17, 18, 23, 24 }, { 1, 7, 8, 9, 10, 15, 16, 21, 22 }, { 4, 8, 11, 14, 16, 19, 21, 24, 27 }, { 6, 7, 10, 14, 17, 19, 22, 23, 27 }, { 2, 5, 8, 9, 10, 19, 20, 23, 24 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 6, 8, 16, 17, 20, 21, 23, 25 }, { 4, 8, 12, 13, 15, 20, 22, 23, 27 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 } ]; /*od3:=od44; > 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, 5)(2, 3)(4, 8)(11, 21)(12, 22)(13, 15)(14, 16)(17, 26)(18, 25) (2, 7)(5, 6)(8, 27)(10, 18)(12, 22)(13, 23)(14, 16)(17, 26)(19, 21) 165 2-(27, 9, 4) Design with 39 blocks*/ //design no.45 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, 18, 20, 21, 23, 25 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 7, 8, 15, 17, 19, 22, 24, 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, 7, 12, 13, 18, 19, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 6, 8, 11, 14, 17, 20, 23, 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, 17, 22, 24 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 7, 8, 10, 12, 15, 18, 21, 23 }, { 2, 3, 6, 12, 13, 15, 20, 22, 23 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 7, 11, 14, 16, 19, 21, 24 }, { 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, 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:= [ { 3, 6, 8, 9, 12, 14, 21, 24, 25 }, { 3, 7, 8, 9, 11, 13, 16, 18, 20 }, { 4, 5, 7, 9, 12, 14, 15, 17, 20 }, { 1, 2, 3, 4, 5, 8, 9, 19, 23 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 1, 3, 4, 6, 7, 12, 16, 26, 27 }, { 1, 5, 6, 11, 14, 16, 20, 21, 23 }, { 2, 4, 11, 16, 17, 19, 20, 22, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 1, 6, 8, 10, 13, 16, 19, 22, 25 }, { 1, 2, 6, 9, 15, 16, 17, 18, 24 }, { 4, 6, 8, 17, 18, 20, 23, 25, 26 }, { 3, 5, 6, 10, 11, 12, 17, 18, 19 }, { 2, 4, 7, 12, 13, 18, 19, 24, 25 }, { 2, 5, 6, 7, 8, 11, 15, 25, 27 }, { 1, 8, 12, 15, 18, 19, 20, 21, 27 }, { 3, 8, 9, 10, 15, 17, 22, 26, 27 }, { 3, 5, 7, 15, 16, 19, 21, 22, 24 }, { 2, 3, 11, 18, 21, 23, 24, 26, 27 }, { 10, 11, 12, 15, 16, 20, 24, 25, 26 }, { 1, 7, 8, 11, 14, 17, 19, 24, 26 }, { 1, 2, 7, 9, 20, 21, 22, 25, 26 }, { 2, 5, 8, 12, 13, 16, 17, 21, 26 }, { 9, 12, 14, 16, 18, 19, 22, 23, 26 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 1, 5, 7, 10, 13, 15, 18, 23, 26 }, { 4, 5, 9, 10, 16, 18, 21, 25, 27 }, { 2, 3, 7, 10, 14, 16, 17, 23, 25 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 2, 3, 6, 12, 13, 15, 20, 22, 23 }, { 6, 7, 9, 10, 19, 20, 23, 24, 27 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 5, 12, 17, 22, 23, 24, 25, 27 }, { 4, 7, 8, 10, 11, 12, 21, 22, 23 }, { 4, 5, 6, 9, 11, 13, 22, 24, 26 }, { 2, 4, 6, 10, 14, 15, 19, 21, 26 }, { 1, 3, 4, 10, 13, 17, 20, 21, 24 }, { 9, 11, 13, 15, 17, 19, 21, 23, 25 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 } ]; /* od3:=od45; > 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, 3)(2, 5)(6, 7)(11, 15)(12, 16)(13, 21)(14, 22)(19, 23)(20, 24) (3, 4)(5, 8)(6, 7)(15, 25)(16, 26)(17, 21)(18, 22)(19, 23)(20, 24) 165 2-(27, 9, 4) Design with 39 blocks */ //design no. 46 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, 18, 20, 21, 23, 25 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 7, 8, 15, 17, 19, 22, 24, 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, 6, 10, 12, 14, 15, 17, 19 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 7, 8, 9, 11, 13, 16, 18, 20 }, { 2, 4, 7, 12, 13, 18, 19, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 6, 8, 11, 14, 17, 20, 23, 26 }, { 2, 4, 7, 9, 14, 15, 20, 21, 26 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 1, 6, 8, 10, 13, 16, 19, 22, 25 }, { 2, 4, 6, 9, 11, 16, 17, 22, 24 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 7, 8, 10, 12, 15, 18, 21, 23 }, { 2, 3, 6, 12, 13, 15, 20, 22, 23 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 7, 11, 14, 16, 19, 21, 24 }, { 2, 3, 6, 10, 11, 18, 19, 21, 26 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 1, 5, 7, 9, 12, 17, 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, 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:= [ { 3, 6, 8, 9, 12, 14, 21, 24, 25 }, { 3, 7, 8, 9, 11, 13, 16, 18, 20 }, { 4, 5, 7, 9, 12, 14, 15, 17, 20 }, { 1, 2, 3, 4, 5, 8, 9, 19, 23 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 1, 3, 4, 6, 7, 12, 16, 26, 27 }, { 1, 5, 6, 11, 14, 16, 20, 21, 23 }, { 2, 4, 11, 16, 17, 19, 20, 22, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 1, 6, 8, 10, 13, 16, 19, 22, 25 }, { 1, 2, 6, 9, 15, 16, 17, 18, 24 }, { 4, 6, 8, 17, 18, 20, 23, 25, 26 }, { 3, 5, 6, 10, 11, 12, 17, 18, 19 }, { 2, 4, 7, 12, 13, 18, 19, 24, 25 }, { 2, 5, 6, 7, 8, 11, 15, 25, 27 }, { 1, 8, 12, 15, 18, 19, 20, 21, 27 }, { 3, 8, 9, 10, 15, 17, 22, 26, 27 }, { 3, 5, 7, 15, 16, 19, 21, 22, 24 }, { 2, 3, 11, 18, 21, 23, 24, 26, 27 }, { 10, 11, 12, 15, 16, 20, 24, 25, 26 }, { 1, 7, 8, 11, 14, 17, 19, 24, 26 }, { 1, 2, 7, 9, 20, 21, 22, 25, 26 }, { 2, 5, 8, 12, 13, 16, 17, 21, 26 }, { 9, 12, 14, 16, 18, 19, 22, 23, 26 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 1, 5, 7, 10, 13, 15, 18, 23, 26 }, { 4, 5, 9, 10, 16, 18, 21, 25, 27 }, { 2, 3, 7, 10, 14, 16, 17, 23, 25 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 2, 3, 6, 12, 13, 15, 20, 22, 23 }, { 6, 7, 9, 10, 19, 20, 23, 24, 27 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 5, 12, 17, 22, 23, 24, 25, 27 }, { 4, 7, 8, 10, 11, 12, 21, 22, 23 }, { 4, 5, 6, 9, 11, 13, 22, 24, 26 }, { 2, 4, 6, 10, 14, 15, 19, 21, 26 }, { 1, 3, 4, 10, 13, 17, 20, 21, 24 }, { 9, 11, 13, 15, 17, 19, 21, 23, 25 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 } ]; /*load "AD41-50.m"; Loading "AD41-50.m" > od3:=od46; > 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, 3)(2, 8, 5)(11, 25, 15)(12, 26, 16)(13, 17, 21)(14, 18, 22) (3, 4)(5, 8)(6, 7)(9, 23)(10, 24)(11, 25)(12, 26)(13, 21)(14, 22) 165 2-(27, 9, 4) Design with 39 blocks */ //design no.47 ablox:= [ { 10, 11, 12, 15, 16, 20, 24, 25, 26 }, { 1, 2, 3, 4, 5, 6, 7, 8, 27 }, { 9, 13, 14, 17, 18, 19, 21, 22, 23 }, { 4, 5, 7, 16, 18, 20, 21, 23, 25 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 6, 8, 15, 17, 19, 22, 24, 26 }, { 4, 5, 6, 9, 11, 14, 21, 24, 26 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 3, 7, 8, 10, 12, 13, 22, 23, 25 }, { 4, 5, 7, 10, 12, 14, 15, 17, 19 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 6, 8, 9, 11, 13, 16, 18, 20 }, { 2, 4, 6, 12, 13, 18, 19, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 7, 8, 11, 14, 17, 20, 23, 26 }, { 2, 4, 7, 9, 13, 15, 20, 22, 26 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 1, 6, 8, 10, 14, 16, 19, 21, 25 }, { 2, 4, 6, 10, 11, 16, 17, 22, 23 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 7, 8, 9, 12, 15, 18, 21, 24 }, { 2, 3, 6, 12, 14, 15, 20, 21, 23 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 7, 11, 13, 16, 19, 22, 24 }, { 2, 3, 7, 10, 11, 18, 19, 21, 26 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 1, 5, 6, 9, 12, 17, 20, 22, 25 }, { 2, 3, 7, 9, 14, 16, 17, 24, 25 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 5, 6, 10, 13, 15, 18, 23, 26 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 6, 7, 9, 11, 15, 19, 23, 25, 27 }, { 1, 3, 4, 12, 13, 16, 17, 21, 26 }, { 2, 5, 8, 9, 12, 16, 19, 23, 26 }, { 6, 7, 10, 13, 17, 20, 21, 24, 27 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 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:= [ { 2, 3, 7, 12, 13, 15, 20, 22, 23 }, { 3, 5, 6, 11, 12, 14, 21, 23, 24 }, { 6, 7, 11, 12, 15, 16, 25, 26, 27 }, { 2, 3, 6, 9, 13, 16, 18, 24, 25 }, { 4, 5, 9, 11, 17, 18, 24, 26, 27 }, { 2, 5, 8, 12, 14, 16, 18, 22, 26 }, { 9, 10, 14, 18, 19, 20, 22, 23, 24 }, { 4, 7, 8, 9, 10, 13, 22, 25, 26 }, { 3, 6, 8, 15, 17, 19, 22, 24, 26 }, { 1, 5, 7, 11, 13, 16, 19, 22, 24 }, { 3, 7, 8, 9, 11, 14, 16, 17, 20 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 4, 5, 7, 10, 12, 14, 15, 17, 19 }, { 1, 2, 7, 14, 17, 23, 24, 25, 26 }, { 4, 5, 6, 16, 17, 20, 22, 23, 25 }, { 2, 5, 8, 10, 11, 15, 20, 24, 25 }, { 3, 5, 7, 18, 19, 20, 21, 25, 26 }, { 1, 8, 11, 20, 21, 22, 23, 26, 27 }, { 1, 2, 6, 9, 10, 11, 12, 17, 22 }, { 1, 3, 4, 9, 12, 16, 19, 23, 26 }, { 10, 12, 13, 16, 17, 20, 21, 24, 26 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 4, 6, 8, 11, 12, 13, 18, 19, 20 }, { 1, 7, 8, 9, 12, 15, 18, 21, 24 }, { 2, 4, 6, 9, 14, 15, 20, 21, 26 }, { 1, 2, 3, 4, 5, 8, 13, 17, 21 }, { 1, 5, 6, 10, 13, 15, 18, 23, 26 }, { 2, 3, 10, 11, 13, 14, 19, 26, 27 }, { 1, 6, 8, 10, 14, 16, 19, 21, 25 }, { 2, 4, 7, 10, 11, 16, 18, 21, 23 }, { 9, 11, 13, 15, 17, 19, 21, 23, 25 }, { 1, 5, 9, 12, 13, 14, 20, 25, 27 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 2, 4, 12, 19, 21, 22, 24, 25, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 3, 8, 10, 12, 17, 18, 23, 25, 27 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 2, 5, 6, 7, 8, 9, 19, 23, 27 }, { 1, 3, 4, 6, 7, 10, 20, 24, 27 } ]; /* load "AD41-50.m"; Loading "AD41-50.m" > od3:=od47; > 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)(2, 8)(6, 7)(9, 19)(10, 20)(13, 21)(14, 22)(15, 25)(16, 26) (3, 4)(5, 8)(6, 7)(9, 23)(10, 24)(11, 25)(12, 26)(13, 21)(14, 22) 165 2-(27, 9, 4) Design with 39 blocks */ //design no.48 ablox:= [ { 10, 11, 12, 15, 16, 20, 24, 25, 26 }, { 1, 2, 3, 4, 5, 6, 7, 8, 27 }, { 9, 13, 14, 17, 18, 19, 21, 22, 23 }, { 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, 10, 14, 18, 20, 22, 24 }, { 6, 7, 9, 11, 15, 19, 23, 25, 27 }, { 1, 3, 4, 12, 13, 16, 17, 21, 26 }, { 2, 5, 8, 9, 12, 16, 19, 23, 26 }, { 6, 7, 10, 13, 17, 20, 21, 24, 27 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 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:= [ { 1, 8, 11, 19, 21, 22, 24, 26, 27 }, { 2, 3, 6, 12, 14, 15, 19, 21, 24 }, { 2, 3, 10, 16, 21, 22, 23, 25, 27 }, { 1, 2, 7, 14, 17, 23, 24, 25, 26 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 4, 5, 7, 16, 18, 19, 21, 24, 25 }, { 1, 5, 7, 11, 13, 16, 20, 22, 23 }, { 1, 2, 6, 9, 10, 11, 12, 17, 22 }, { 4, 5, 6, 10, 11, 14, 21, 23, 26 }, { 1, 3, 4, 10, 12, 16, 20, 24, 26 }, { 3, 8, 13, 14, 15, 20, 23, 26, 27 }, { 3, 5, 6, 17, 19, 20, 22, 25, 26 }, { 2, 3, 7, 9, 11, 18, 20, 21, 26 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 7, 8, 10, 12, 15, 18, 21, 23 }, { 2, 5, 6, 7, 8, 12, 16, 26, 27 }, { 4, 6, 8, 15, 16, 17, 22, 23, 24 }, { 1, 3, 4, 6, 7, 9, 19, 23, 27 }, { 6, 7, 10, 11, 15, 20, 24, 25, 27 }, { 11, 12, 13, 15, 16, 17, 21, 25, 26 }, { 3, 7, 8, 9, 12, 13, 22, 24, 25 }, { 3, 6, 8, 10, 11, 13, 16, 18, 19 }, { 1, 2, 3, 4, 5, 8, 13, 17, 21 }, { 9, 10, 13, 17, 19, 20, 21, 23, 24 }, { 9, 12, 14, 16, 18, 19, 22, 23, 26 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 1, 5, 6, 9, 13, 15, 18, 24, 26 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 2, 5, 8, 9, 11, 15, 19, 23, 25 }, { 1, 6, 8, 9, 14, 16, 20, 21, 25 }, { 3, 5, 7, 9, 10, 14, 15, 16, 17 }, { 2, 4, 7, 10, 13, 15, 19, 22, 26 }, { 1, 5, 10, 12, 13, 14, 19, 25, 27 }, { 2, 4, 6, 12, 13, 18, 20, 23, 25 }, { 4, 7, 8, 11, 12, 14, 17, 19, 20 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 2, 4, 9, 11, 13, 14, 16, 24, 27 }, { 4, 5, 9, 12, 15, 20, 21, 22, 27 } ]; /* load "AD41-50.m"; Loading "AD41-50.m" > od3:=od48; > 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)(2, 8)(6, 7)(11, 25)(12, 26)(13, 17)(14, 18)(19, 23)(20, 24) (3, 4)(5, 8)(6, 7)(9, 19)(10, 20)(11, 15)(12, 16)(13, 17)(14, 18) 165 2-(27, 9, 4) Design with 39 blocks*/ //design no.49 ablox:= [ { 10, 11, 12, 15, 16, 20, 24, 25, 26 }, { 1, 2, 3, 4, 5, 6, 7, 8, 27 }, { 9, 13, 14, 17, 18, 19, 21, 22, 23 }, { 4, 5, 6, 16, 17, 20, 22, 23, 25 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 7, 8, 15, 18, 19, 21, 24, 26 }, { 4, 5, 6, 9, 11, 14, 21, 24, 26 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 3, 7, 8, 10, 12, 13, 22, 23, 25 }, { 4, 5, 7, 10, 12, 14, 15, 17, 19 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 6, 8, 9, 11, 13, 16, 18, 20 }, { 2, 4, 6, 12, 13, 18, 19, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 7, 8, 11, 14, 17, 20, 23, 26 }, { 2, 4, 7, 9, 13, 15, 20, 22, 26 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 1, 6, 8, 10, 14, 16, 19, 21, 25 }, { 2, 4, 7, 10, 11, 16, 18, 21, 23 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 6, 8, 9, 12, 15, 17, 22, 24 }, { 2, 3, 6, 12, 14, 15, 20, 21, 23 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 7, 11, 13, 16, 19, 22, 24 }, { 2, 3, 6, 10, 11, 17, 19, 22, 26 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 1, 5, 7, 9, 12, 18, 20, 21, 25 }, { 2, 3, 7, 9, 14, 16, 17, 24, 25 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 5, 6, 10, 13, 15, 18, 23, 26 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 6, 7, 9, 11, 15, 19, 23, 25, 27 }, { 1, 3, 4, 12, 13, 16, 17, 21, 26 }, { 2, 5, 8, 9, 12, 16, 19, 23, 26 }, { 6, 7, 10, 13, 17, 20, 21, 24, 27 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 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:= [ { 2, 3, 7, 12, 13, 15, 20, 22, 23 }, { 3, 5, 6, 11, 12, 14, 21, 23, 24 }, { 6, 7, 11, 12, 15, 16, 25, 26, 27 }, { 2, 3, 6, 9, 13, 16, 18, 24, 25 }, { 4, 5, 9, 11, 17, 18, 24, 26, 27 }, { 2, 5, 8, 12, 14, 16, 18, 22, 26 }, { 9, 10, 14, 18, 19, 20, 22, 23, 24 }, { 4, 7, 8, 9, 10, 13, 22, 25, 26 }, { 3, 6, 8, 15, 17, 19, 22, 24, 26 }, { 1, 5, 7, 11, 13, 16, 19, 22, 24 }, { 3, 7, 8, 9, 11, 14, 16, 17, 20 }, { 1, 3, 4, 11, 14, 15, 18, 22, 25 }, { 4, 5, 7, 10, 12, 14, 15, 17, 19 }, { 1, 2, 7, 14, 17, 23, 24, 25, 26 }, { 4, 5, 6, 16, 17, 20, 22, 23, 25 }, { 2, 5, 8, 10, 11, 15, 20, 24, 25 }, { 3, 5, 7, 18, 19, 20, 21, 25, 26 }, { 1, 8, 11, 20, 21, 22, 23, 26, 27 }, { 1, 2, 6, 9, 10, 11, 12, 17, 22 }, { 1, 3, 4, 9, 12, 16, 19, 23, 26 }, { 10, 12, 13, 16, 17, 20, 21, 24, 26 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 4, 6, 8, 11, 12, 13, 18, 19, 20 }, { 1, 7, 8, 9, 12, 15, 18, 21, 24 }, { 2, 4, 6, 9, 14, 15, 20, 21, 26 }, { 1, 2, 3, 4, 5, 8, 13, 17, 21 }, { 1, 5, 6, 10, 13, 15, 18, 23, 26 }, { 2, 3, 10, 11, 13, 14, 19, 26, 27 }, { 1, 6, 8, 10, 14, 16, 19, 21, 25 }, { 2, 4, 7, 10, 11, 16, 18, 21, 23 }, { 9, 11, 13, 15, 17, 19, 21, 23, 25 }, { 1, 5, 9, 12, 13, 14, 20, 25, 27 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 2, 4, 12, 19, 21, 22, 24, 25, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 3, 8, 10, 12, 17, 18, 23, 25, 27 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 2, 5, 6, 7, 8, 9, 19, 23, 27 }, { 1, 3, 4, 6, 7, 10, 20, 24, 27 } ]; /*load "AD41-50.m"; Loading "AD41-50.m" > od3:=od49; > 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)(2, 8)(6, 7)(11, 25)(12, 26)(13, 17)(14, 18)(19, 23)(20, 24) (3, 4)(5, 8)(6, 7)(9, 19)(10, 20)(11, 15)(12, 16)(13, 17)(14, 18) 165 2-(27, 9, 4) Design with 39 blocks */