//design no. 30 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, 17, 20, 22, 23, 25 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 6, 8, 15, 18, 19, 21, 24, 26 }, { 4, 5, 7, 9, 11, 14, 21, 24, 26 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 3, 6, 8, 10, 12, 13, 22, 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, 22, 26 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 1, 7, 8, 10, 14, 16, 19, 21, 25 }, { 2, 4, 6, 10, 11, 16, 18, 21, 23 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 7, 8, 9, 12, 15, 17, 22, 24 }, { 2, 3, 7, 11, 13, 16, 19, 22, 24 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 6, 12, 14, 15, 20, 21, 23 }, { 2, 3, 7, 9, 12, 18, 20, 21, 25 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 1, 5, 6, 10, 11, 17, 19, 22, 26 }, { 2, 3, 7, 10, 14, 15, 17, 23, 26 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 5, 6, 9, 13, 16, 18, 24, 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, 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 n the code blos:= [ { 4, 5, 7, 21, 22, 23, 24, 25, 26 }, { 1, 2, 16, 17, 20, 22, 23, 25, 27 }, { 1, 5, 6, 10, 11, 17, 19, 22, 26 }, { 3, 6, 8, 15, 16, 17, 18, 19, 20 }, { 1, 7, 8, 10, 11, 16, 18, 21, 23 }, { 6, 7, 11, 12, 15, 16, 25, 26, 27 }, { 6, 7, 10, 14, 18, 20, 22, 24, 27 }, { 2, 4, 6, 11, 13, 18, 20, 23, 26 }, { 2, 4, 6, 12, 14, 17, 19, 24, 25 }, { 2, 3, 7, 12, 14, 15, 20, 21, 23 }, { 3, 5, 9, 13, 15, 20, 22, 26, 27 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 3, 6, 8, 10, 12, 13, 22, 23, 25 }, { 4, 8, 9, 13, 16, 18, 24, 25, 27 }, { 10, 12, 13, 16, 17, 20, 21, 24, 26 }, { 2, 4, 6, 9, 10, 15, 16, 21, 22 }, { 3, 5, 10, 14, 16, 19, 21, 25, 27 }, { 1, 3, 4, 9, 12, 16, 19, 23, 26 }, { 4, 5, 7, 9, 11, 14, 16, 17, 20 }, { 2, 3, 7, 11, 13, 16, 19, 22, 24 }, { 1, 3, 4, 13, 14, 17, 18, 21, 22 }, { 9, 11, 14, 15, 18, 19, 22, 23, 25 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 4, 8, 10, 14, 15, 17, 23, 26, 27 }, { 1, 5, 6, 9, 12, 18, 20, 21, 25 }, { 1, 2, 3, 4, 5, 6, 7, 8, 27 }, { 4, 5, 7, 10, 12, 13, 15, 18, 19 }, { 2, 5, 8, 12, 14, 16, 18, 22, 26 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 2, 15, 18, 19, 21, 24, 26, 27 }, { 3, 6, 8, 9, 11, 14, 21, 24, 26 }, { 1, 5, 6, 13, 14, 15, 16, 23, 24 }, { 1, 3, 4, 10, 11, 15, 20, 24, 25 }, { 1, 7, 8, 13, 14, 19, 20, 25, 26 }, { 2, 5, 8, 11, 13, 15, 17, 21, 25 }, { 6, 7, 9, 13, 17, 19, 21, 23, 27 }, { 2, 5, 8, 9, 10, 19, 20, 23, 24 }, { 2, 3, 7, 9, 10, 17, 18, 25, 26 }, { 1, 7, 8, 9, 12, 15, 17, 22, 24 } ]; /* load "AD21-30.m"; Loading "AD21-30.m" > od3:=od30; > 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 = 12 = 2^2 * 3 (1, 5)(2, 3)(4, 8)(11, 22)(12, 21)(13, 16)(14, 15)(17, 26)(18, 25) (1, 2)(3, 5)(4, 8)(6, 7)(11, 14)(12, 13)(15, 22)(16, 21)(17, 26)(18, 25)(19, 23)(20, 24) (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 31n (corrected) > 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, 15, 18, 20, 21, 23, 26 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 3, 7, 8, 16, 17, 19, 22, 24, 25 }, { 4, 5, 7, 10, 12, 13, 22, 23, 25 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 3, 6, 8, 9, 11, 14, 21, 24, 26 }, { 4, 5, 7, 9, 11, 14, 16, 17, 20 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 6, 8, 10, 12, 13, 15, 18, 19 }, { 2, 4, 7, 11, 13, 18, 19, 24, 26 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 6, 8, 12, 14, 17, 20, 23, 25 }, { 2, 4, 6, 10, 14, 16, 19, 21, 25 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 1, 7, 8, 9, 13, 15, 20, 22, 26 }, { 2, 4, 6, 9, 12, 15, 17, 22, 24 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 1, 7, 8, 10, 11, 16, 18, 21, 23 }, { 2, 3, 6, 11, 13, 16, 20, 22, 23 }, { 4, 8, 9, 10, 17, 18, 25, 26, 27 }, { 1, 5, 7, 12, 14, 15, 19, 21, 24 }, { 2, 3, 7, 9, 12, 18, 20, 21, 25 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 1, 5, 6, 10, 11, 17, 19, 22, 26 }, { 2, 3, 7, 10, 14, 15, 17, 23, 26 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 5, 6, 9, 13, 16, 18, 24, 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, 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 of 31n > blos; [ { 9, 12, 13, 16, 17, 19, 21, 23, 26 }, { 2, 3, 6, 11, 13, 16, 20, 22, 23 }, { 1, 2, 3, 4, 5, 8, 9, 19, 23 }, { 1, 2, 9, 10, 11, 12, 13, 14, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 3, 8, 9, 10, 16, 17, 22, 25, 27 }, { 4, 6, 8, 17, 18, 20, 23, 25, 26 }, { 1, 2, 6, 9, 15, 16, 17, 18, 24 }, { 3, 5, 6, 10, 11, 12, 17, 18, 19 }, { 4, 5, 6, 9, 12, 13, 22, 24, 25 }, { 1, 5, 11, 17, 22, 23, 24, 26, 27 }, { 1, 6, 8, 10, 13, 15, 19, 22, 26 }, { 9, 11, 14, 15, 18, 19, 22, 23, 25 }, { 3, 5, 7, 15, 16, 19, 21, 22, 24 }, { 2, 5, 8, 11, 13, 15, 17, 21, 25 }, { 1, 5, 7, 10, 13, 16, 18, 23, 25 }, { 2, 5, 6, 7, 8, 12, 16, 26, 27 }, { 10, 11, 12, 15, 16, 20, 24, 25, 26 }, { 4, 5, 7, 9, 11, 14, 16, 17, 20 }, { 1, 2, 7, 9, 20, 21, 22, 25, 26 }, { 3, 6, 8, 9, 11, 14, 21, 24, 26 }, { 3, 7, 8, 9, 12, 13, 15, 18, 20 }, { 1, 3, 4, 12, 14, 16, 18, 22, 26 }, { 2, 5, 8, 10, 14, 18, 20, 22, 24 }, { 6, 7, 9, 10, 19, 20, 23, 24, 27 }, { 3, 5, 13, 14, 19, 20, 25, 26, 27 }, { 4, 5, 9, 10, 15, 18, 21, 26, 27 }, { 1, 5, 6, 12, 14, 15, 20, 21, 23 }, { 2, 4, 12, 15, 17, 19, 20, 22, 27 }, { 1, 8, 11, 16, 18, 19, 20, 21, 27 }, { 2, 3, 7, 10, 14, 15, 17, 23, 26 }, { 2, 4, 6, 10, 14, 16, 19, 21, 25 }, { 2, 4, 7, 11, 13, 18, 19, 24, 26 }, { 4, 7, 8, 10, 11, 12, 21, 22, 23 }, { 2, 3, 12, 18, 21, 23, 24, 25, 27 }, { 1, 3, 4, 10, 13, 17, 20, 21, 24 }, { 1, 7, 8, 12, 14, 17, 19, 24, 25 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 1, 3, 4, 6, 7, 11, 15, 25, 27 } ] > /* > od3:=od31n; > > 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 = 12 = 2^2 * 3 > (1, 3)(2, 5)(6, 7)(11, 15)(12, 16)(13, 21)(14, 22)(19, 23)(20, 24) > (1, 2)(3, 8)(4, 5)(11, 14)(12, 13)(15, 18)(16, 17)(21, 26)(22, 25) > (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 */ > load "AD21-30.m"; Loading "AD21-30.m" > od3:=od30; > c31n; [27, 13, 6] Linear Code over GF(3) Generator matrix: [1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 2 1 0 2 2 0 0 2 2 1 2 1] [0 1 0 0 0 0 0 2 0 0 0 0 0 2 0 1 2 0 1 1 1 1 2 2 0 2 0] [0 0 1 0 0 0 0 1 0 0 0 0 0 2 0 1 1 2 2 2 0 0 2 2 1 0 1] [0 0 0 1 0 0 0 1 0 0 0 0 0 2 0 0 1 0 2 2 0 2 2 2 1 1 1] [0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 2 1 2 2 2 2 1 1 1 0 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 2 0 1 2 1 0 0 2] [0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 2 1 0 1 1 2 0 0 2] [0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 2 1 0 0 2 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 2 0 1 0 2 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 2 2 1 2 2 1 0 1 1 2 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 1 0 2 0 0 0 2 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 1 2 0 0 1 2 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 0] > 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 = 12 = 2^2 * 3 (1, 5)(2, 3)(4, 8)(11, 22)(12, 21)(13, 16)(14, 15)(17, 26)(18, 25) (1, 2)(3, 5)(4, 8)(6, 7)(11, 14)(12, 13)(15, 22)(16, 21)(17, 26)(18, 25)(19, 23)(20, 24) (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 > c30:=C; > IsEquivalent(c30,c31n); true Mapping from: ModTupFld: V to ModTupFld: V > c30 eq c31n; false > load "lamton.fu"; Loading "lamton.fu" > load "dualbl.fu"; >> load "dualbl.fu"; ^ User error: Could not open file "dualbl.fu" (No such file or directory) > dualbl > ; function(v, bloxset) ... end function > d31:=dcode(lamton(od31n)); > WD(d31); [ <0, 1>, <6, 10>, <9, 4>, <12, 162>, <13, 114>, <15, 492>, <16, 1320>, <18, 10008>, <19, 20616>, <21, 46008>, <22, 185802>, <24, 160932>, <25, 398364>, <27, 212006>, <28, 335148>, <30, 95256>, <31, 114270>, <33, 6236>, <34, 6936>, <36, 326>, <37, 312> ] > quit; Total time: 151.819 seconds From fleming@math.clemson.edu Tue Mar 30 08:35:13 1999 Date: Mon, 29 Mar 1999 10:09:35 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton32 lamton32 > 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, 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, 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, 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 } ] From fleming@math.clemson.edu Tue Mar 30 08:35:34 1999 Date: Mon, 29 Mar 1999 10:10:43 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton33 lamton33 > 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, 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, 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, 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 } ] //design no. 34 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, 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, 6, 10, 12, 13, 15, 18, 19 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 3, 7, 8, 9, 11, 14, 16, 17, 20 }, { 2, 4, 7, 12, 14, 17, 19, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 6, 8, 11, 13, 18, 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, 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, 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, 10, 13, 16, 18, 23, 25 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 5, 6, 9, 14, 15, 17, 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, 7, 8, 9, 14, 16, 20, 21, 25 }, { 3, 6, 8, 10, 11, 14, 16, 17, 19 }, { 2, 4, 7, 9, 13, 15, 20, 22, 26 }, { 4, 8, 13, 14, 15, 16, 23, 24, 27 }, { 3, 5, 7, 9, 11, 12, 17, 18, 20 }, { 1, 3, 4, 6, 7, 14, 18, 22, 27 }, { 4, 6, 8, 17, 18, 20, 23, 25, 26 }, { 1, 3, 4, 10, 12, 16, 20, 24, 26 }, { 3, 8, 12, 13, 19, 20, 22, 25, 27 }, { 3, 7, 8, 15, 18, 19, 21, 24, 26 }, { 1, 2, 6, 10, 19, 21, 22, 25, 26 }, { 10, 13, 14, 17, 18, 20, 21, 22, 24 }, { 2, 3, 6, 12, 14, 15, 20, 21, 23 }, { 4, 5, 11, 14, 19, 20, 21, 26, 27 }, { 6, 7, 11, 12, 15, 16, 25, 26, 27 }, { 1, 5, 12, 18, 21, 23, 24, 25, 27 }, { 9, 11, 14, 15, 18, 19, 22, 23, 25 }, { 1, 5, 7, 10, 14, 15, 17, 23, 26 }, { 6, 7, 9, 10, 19, 20, 23, 24, 27 }, { 9, 12, 13, 16, 17, 19, 21, 23, 26 }, { 1, 6, 8, 9, 12, 15, 17, 22, 24 }, { 1, 3, 4, 11, 13, 15, 17, 21, 25 }, { 2, 4, 9, 10, 12, 14, 17, 25, 27 }, { 4, 5, 7, 16, 17, 19, 22, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 2, 3, 11, 17, 22, 23, 24, 26, 27 }, { 2, 5, 8, 12, 14, 16, 18, 22, 26 }, { 1, 8, 9, 10, 11, 13, 18, 26, 27 }, { 2, 3, 7, 10, 13, 16, 18, 23, 25 }, { 1, 5, 6, 11, 13, 16, 20, 22, 23 }, { 1, 2, 7, 11, 12, 13, 14, 19, 24 }, { 4, 7, 8, 10, 11, 12, 21, 22, 23 }, { 2, 4, 6, 9, 11, 16, 18, 21, 24 }, { 1, 2, 15, 16, 17, 18, 19, 20, 27 }, { 1, 2, 3, 4, 5, 8, 9, 19, 23 }, { 3, 5, 6, 9, 13, 14, 24, 25, 26 }, { 2, 5, 8, 10, 11, 15, 20, 24, 25 }, { 2, 5, 6, 7, 8, 13, 17, 21, 27 }, { 4, 5, 6, 10, 12, 13, 15, 18, 19 } ]; /* > 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 = 12 = 2^2 * 3 (9, 24)(10, 23)(11, 21)(12, 22)(13, 25)(14, 26)(15, 17)(16, 18)(19, 20) (1, 4)(2, 8)(6, 7)(9, 23)(10, 24)(11, 15)(12, 16)(17, 21)(18, 22) (3, 4)(5, 8)(6, 7)(9, 10)(11, 13)(12, 14)(15, 17)(16, 18)(19, 20)(21, 25)(22, 26)(23, 24) 165 2-(27, 9, 4) Design with 39 blocks */ aades:=Design<2,27|ablox>; nndes:=Design<2,27|blos>; From fleming@math.clemson.edu Tue Mar 30 08:36:00 1999 Date: Mon, 29 Mar 1999 10:11:47 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton35 lamton35 > 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 } ] > 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, 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 } ] //design no.36 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, 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, 7, 12, 14, 17, 19, 24, 25 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 1, 6, 8, 11, 13, 18, 20, 23, 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, 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, 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, 13, 16, 18, 23, 25 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 1, 5, 6, 9, 14, 15, 17, 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:= [ { 3, 6, 8, 15, 18, 20, 21, 23, 26 }, { 2, 3, 7, 12, 14, 15, 19, 21, 24 }, { 1, 2, 21, 22, 23, 24, 25, 26, 27 }, { 1, 2, 7, 10, 15, 16, 17, 18, 23 }, { 2, 4, 6, 9, 11, 16, 18, 21, 24 }, { 1, 3, 4, 10, 14, 18, 20, 22, 24 }, { 1, 5, 6, 10, 12, 18, 19, 21, 25 }, { 2, 4, 7, 9, 13, 15, 20, 22, 26 }, { 2, 5, 6, 7, 8, 11, 15, 25, 27 }, { 10, 11, 12, 15, 16, 20, 24, 25, 26 }, { 1, 2, 6, 11, 12, 13, 14, 20, 23 }, { 3, 5, 9, 10, 15, 16, 21, 22, 27 }, { 3, 5, 7, 9, 11, 12, 17, 18, 20 }, { 4, 5, 6, 16, 17, 20, 22, 23, 25 }, { 1, 3, 4, 11, 13, 15, 17, 21, 25 }, { 4, 7, 8, 17, 18, 19, 24, 25, 26 }, { 2, 3, 6, 10, 11, 17, 19, 22, 26 }, { 1, 6, 8, 9, 12, 15, 17, 22, 24 }, { 2, 3, 13, 16, 18, 19, 20, 25, 27 }, { 1, 8, 9, 10, 11, 13, 18, 26, 27 }, { 4, 6, 8, 10, 13, 14, 15, 16, 19 }, { 3, 8, 11, 14, 16, 17, 23, 24, 27 }, { 2, 5, 8, 10, 13, 17, 20, 21, 24 }, { 9, 12, 13, 16, 17, 19, 21, 23, 26 }, { 1, 3, 4, 6, 7, 12, 16, 26, 27 }, { 1, 7, 8, 9, 14, 16, 20, 21, 25 }, { 9, 11, 14, 15, 18, 19, 22, 23, 25 }, { 6, 7, 9, 10, 19, 20, 23, 24, 27 }, { 1, 2, 3, 4, 5, 8, 9, 19, 23 }, { 1, 5, 14, 15, 17, 19, 20, 26, 27 }, { 4, 5, 12, 13, 15, 18, 23, 24, 27 }, { 2, 5, 8, 12, 14, 16, 18, 22, 26 }, { 4, 8, 11, 12, 19, 20, 21, 22, 27 }, { 2, 4, 9, 10, 12, 14, 17, 25, 27 }, { 6, 7, 13, 14, 17, 18, 21, 22, 27 }, { 3, 5, 6, 9, 13, 14, 24, 25, 26 }, { 3, 7, 8, 10, 12, 13, 22, 23, 25 }, { 4, 5, 7, 10, 11, 14, 21, 23, 26 }, { 1, 5, 7, 11, 13, 16, 19, 22, 24 } ]; /*> 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 = 12 = 2^2 * 3 (1, 3)(2, 5)(6, 7)(11, 15)(12, 16)(13, 21)(14, 22)(19, 23)(20, 24) (9, 10)(11, 13)(12, 14)(15, 21)(16, 22)(17, 25)(18, 26)(19, 24)(20, 23) (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 */ aades:=Design<2,27|ablox>; nndes:=Design<2,27|blos>; From fleming@math.clemson.edu Tue Mar 30 08:39:20 1999 Date: Mon, 29 Mar 1999 10:13:16 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton37 lamton37 > 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 } ] > 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, 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 } ] From fleming@math.clemson.edu Tue Mar 30 08:39:36 1999 Date: Mon, 29 Mar 1999 10:14:17 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton38 lamton38 > blos; [ { 5, 7, 8, 10, 11, 14, 16, 17, 19 }, { 3, 5, 11, 12, 17, 18, 23, 24, 27 }, { 1, 2, 5, 7, 8, 9, 12, 13, 27 }, { 2, 3, 7, 13, 14, 17, 18, 21, 22 }, { 2, 3, 5, 9, 10, 15, 19, 21, 24 }, { 5, 7, 8, 15, 18, 20, 21, 23, 26 }, { 1, 2, 16, 17, 19, 22, 24, 25, 27 }, { 3, 4, 6, 15, 16, 17, 18, 19, 20 }, { 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 }, { 10, 11, 14, 21, 22, 23, 24, 25, 26 }, { 1, 3, 8, 9, 10, 17, 18, 25, 26 }, { 3, 7, 9, 10, 16, 20, 22, 23, 27 }, { 9, 12, 13, 15, 18, 20, 22, 24, 25 }, { 4, 7, 9, 11, 18, 19, 21, 25, 27 }, { 2, 6, 8, 10, 12, 15, 17, 22, 23 }, { 2, 4, 5, 9, 11, 17, 20, 22, 26 }, { 6, 7, 9, 14, 15, 17, 24, 26, 27 }, { 9, 12, 13, 16, 17, 19, 21, 23, 26 }, { 3, 4, 5, 6, 7, 8, 22, 24, 25 }, { 5, 6, 10, 12, 19, 20, 25, 26, 27 }, { 2, 3, 8, 11, 12, 16, 20, 21, 25 }, { 1, 4, 5, 10, 13, 18, 19, 22, 23 }, { 1, 2, 10, 11, 14, 15, 18, 20, 27 }, { 4, 5, 12, 14, 15, 16, 21, 22, 27 }, { 1, 5, 6, 11, 13, 15, 17, 21, 25 }, { 2, 4, 8, 12, 14, 18, 19, 24, 26 }, { 2, 6, 7, 11, 13, 19, 20, 23, 24 }, { 2, 5, 6, 9, 14, 16, 18, 23, 25 }, { 6, 8, 11, 13, 16, 18, 22, 26, 27 }, { 1, 6, 8, 9, 14, 19, 20, 21, 22 }, { 1, 4, 7, 12, 14, 17, 20, 23, 25 }, { 2, 4, 7, 10, 13, 15, 16, 25, 26 }, { 1, 3, 5, 13, 14, 16, 20, 24, 26 }, { 1, 6, 7, 10, 12, 16, 18, 21, 24 }, { 1, 3, 7, 11, 12, 15, 19, 22, 26 }, { 4, 8, 10, 13, 17, 20, 21, 24, 27 }, { 1, 4, 8, 9, 11, 15, 16, 23, 24 } ] > 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, 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 } ] From fleming@math.clemson.edu Tue Mar 30 08:39:51 1999 Date: Mon, 29 Mar 1999 10:15:17 -0500 (EST) From: Kirsten Fleming To: keyj@mathsun.uwc.ac.za Subject: lamton39 lamton39 > 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 } ] > 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, 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 } ]