### This work done by Omar A. AbuGhneim from Jordan University (Email: o_abughneim@yahoo.com). # There are 267 groups of order 64. Among them, there are 259 groups that # admit (64,28,12) difference sets. The other 8 groups do not have any # (64,28,12) difference sets. We wrote programs using the software GAP # to construct all (64,28,12) difference sets in the 259 groups of order # 64 that admit (64,28,12) difference sets. # We refer to the groups as they appear in the SmallGroups library of # the software package GAP. For instance, when we work in groups of # order 64 and write [64,14] we mean group number 14 of order 64 in the # GAP library. # The 8 groups that do not admit (64,28,12) difference sets are # [64, 1], [64, 38], [64, 47], [64, 50], [64, 52], [64, 53], [64, 54], # and [64, 186]. Indeed, these groups are the ones that have either # the cyclic group of order 32 as a factor group or have the dihedral # group of order 32 as a factor group. # Also, we find all (64,28,12) difference sets that are reversible # i.e. all (64,28,12) difference sets D with D=D^(-1). There are 184 # groups of order 64 that have reversible (64,28,12) difference sets. # These groups are [64,i] where i in {2, 3, 4, 5, 8, 9, 10, 11, 12, 13, # 15, 16, 18, 20, 22, 23, 24, 25, 28, 30, 31, 32, 33, 34, 35, 36, 37, 40, # 41, 42, 43, 45, 46, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, # 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 87, # 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, # 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 126, # 127, 128, 129, 130, 131, 133, 134, 135, 138, 140, 141, 142, 144, 145, 146, # 147, 149, 150, 151, 152, 153, 155, 156, 157, 159, 160, 161, 162, 163, 164, # 166, 167, 169, 170, 172, 173, 174, 177, 178, 179, 182, 184, 187, 190, 192, # 193, 194, 195, 196, 197, 199, 200, 202, 203, 204, 205, 206, 207, 208, 209, # 210, 211, 213, 214, 215, 216, 219, 221, 222, 226, 227, 231, 232, 234, 236, # 240, 241, 242, 245, 247, 249, 250, 251, 254, 260, 261, 263, 267 }. # We used the software GAP to find all (64,28,12) difference sets and # reversible (64,28,12) difference sets. # In this file we list all inequivalent (64,28,12) difference sets # in group [64,115]. Also, we determine the nonisomorphic # symmetric (64,28,12) designs that rise from these DSs. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,115]. # To determine the nonisomorphic symmetric (64,28,12) designs, we used # the DESIGN package for GAP, Version 1.6, 2011, by L.H. Soicher, # http://designtheory.org/software/gap design/. # Note: The GAP command 'e:=Elements(SmallGroup(64,115));' can be # used to create a list e of the elements of the group [64,115]. # In our list of (64,28,12) DSs in group [64,115], we have [1, # 2, 3, 4, 5, 7, 8, 10, 13, 16, 17, 18, 21, 32, 34, # 36, 39, 43, 46, 47, 48, 52, 54, 56, 58, 59, 63, 64]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[7], e[8], e[10], e[13], e[16], e[17], e[18], e[21], e[32], e[34], e[36], # e[39], e[43], e[46], e[47], e[48], e[52], e[54], e[56], e[58], e[59], e[63], e[64]] # where e is the list of the elements of the group [64,115] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,115));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 115] ### The number of inequivalent (64,28,12) DSs in group [64,115] is 1624 ### The list of all inequivalent (64,28,12) DSs in group [64,115] is DS115:=[ [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 16, 17, 18, 21, 32, 34, 36, 39, 43, 46, 47, 48, 52, 54, 56, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 16, 17, 18, 21, 25, 32, 36, 39, 43, 47, 52, 53, 54, 55, 56, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 16, 17, 18, 21, 23, 32, 34, 36, 39, 44, 45, 46, 47, 48, 52, 54, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 16, 17, 18, 21, 23, 25, 32, 36, 39, 44, 45, 47, 52, 53, 54, 55, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 17, 18, 21, 26, 32, 34, 35, 37, 39, 43, 45, 46, 52, 55, 56, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 17, 18, 21, 25, 26, 32, 35, 37, 39, 43, 45, 48, 52, 53, 56, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 17, 18, 21, 25, 26, 32, 35, 37, 38, 39, 43, 52, 53, 55, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 17, 18, 21, 23, 26, 32, 34, 35, 37, 39, 44, 46, 52, 55, 56, 59, 61, 64 ], [ 1, 2, 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50, 52, 53, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 28, 29, 33, 36, 37, 39, 40, 50, 55, 56, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 30, 34, 35, 37, 40, 41, 52, 53, 55, 56, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 27, 30, 32, 33, 34, 41, 44, 49, 50, 56, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 27, 28, 33, 34, 41, 44, 46, 48, 49, 50, 56, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 20, 28, 33, 34, 39, 41, 42, 44, 48, 56, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 30, 34, 38, 40, 41, 52, 53, 54, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 28, 33, 34, 39, 40, 41, 44, 46, 48, 56, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 28, 32, 33, 34, 39, 40, 44, 46, 52, 55, 56, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 28, 30, 32, 33, 34, 40, 44, 53, 55, 56, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 23, 28, 29, 33, 37, 38, 39, 40, 50, 55, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 22, 23, 28, 33, 37, 39, 40, 42, 45, 55, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 21, 23, 29, 33, 38, 39, 42, 44, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 18, 21, 29, 33, 38, 40, 42, 43, 44, 45, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 28, 30, 33, 38, 41, 44, 46, 48, 49, 52, 53, 54, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 27, 28, 36, 38, 41, 44, 47, 48, 49, 50, 53, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 27, 28, 30, 33, 38, 41, 44, 47, 48, 50, 52, 53, 54, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 26, 27, 28, 36, 38, 41, 45, 49, 50, 53, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 26, 27, 28, 30, 33, 38, 41, 45, 50, 52, 53, 54, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 23, 27, 30, 32, 36, 38, 41, 45, 49, 50, 53, 56, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 23, 27, 28, 33, 35, 41, 45, 49, 50, 53, 56, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 23, 26, 27, 30, 32, 35, 36, 41, 47, 49, 50, 53, 54, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 28, 29, 33, 34, 35, 36, 37, 45, 56, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 28, 32, 33, 36, 38, 39, 40, 44, 46, 52, 54, 55, 56, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 28, 30, 32, 40, 44, 45, 46, 48, 53, 56, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 28, 30, 32, 33, 34, 36, 38, 40, 44, 54, 56, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 24, 28, 36, 38, 39, 40, 41, 44, 47, 48, 53, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 24, 28, 30, 32, 40, 43, 44, 45, 47, 48, 53, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 24, 26, 28, 36, 38, 39, 40, 41, 45, 53, 56, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 23, 28, 33, 35, 39, 40, 41, 45, 53, 56, 57, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 23, 28, 29, 33, 35, 39, 40, 50, 53, 55, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 23, 24, 26, 28, 30, 32, 40, 45, 53, 56, 57, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 22, 28, 33, 36, 39, 40, 42, 44, 46, 48, 54, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 22, 24, 28, 36, 39, 40, 42, 44, 47, 48, 53, 55, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 22, 24, 26, 28, 36, 39, 40, 42, 45, 53, 55, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 20, 28, 36, 38, 40, 41, 42, 44, 48, 53, 56, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 20, 25, 28, 33, 35, 40, 41, 42, 48, 53, 56, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 22, 27, 33, 36, 37, 41, 42, 44, 46, 50, 54, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 22, 23, 27, 33, 35, 37, 41, 42, 50, 53, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 21, 27, 33, 34, 35, 38, 42, 43, 45, 49, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 21, 27, 28, 33, 38, 42, 43, 45, 51, 53, 54, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 28, 29, 33, 36, 37, 39, 42, 48, 50, 54, 55, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 28, 30, 32, 37, 40, 45, 46, 53, 55, 56, 57, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 27, 28, 29, 36, 37, 38, 40, 45, 46, 56, 57, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 20, 21, 29, 33, 37, 38, 45, 49, 51, 53, 54, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 27, 30, 32, 37, 38, 41, 44, 49, 50, 53, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 27, 28, 37, 38, 41, 44, 46, 48, 49, 50, 53, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 28, 37, 38, 39, 41, 42, 44, 48, 53, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 28, 37, 38, 39, 40, 41, 44, 46, 48, 53, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 28, 32, 37, 38, 39, 40, 44, 46, 52, 53, 55, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 28, 30, 32, 34, 37, 38, 40, 44, 53, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 19, 21, 23, 29, 36, 39, 42, 44, 55, 56, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 21, 29, 36, 40, 42, 43, 44, 45, 55, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 23, 28, 29, 36, 38, 39, 40, 50, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 22, 23, 28, 36, 39, 40, 42, 45, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 28, 29, 33, 38, 42, 43, 45, 49, 53, 54, 57, 61 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1018 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS115[1], DS115[11], DS115[13], DS115[22], DS115[34], DS115[37], DS115[38], DS115[39], DS115[42], DS115[49], DS115[55], DS115[59], DS115[67], DS115[68], DS115[75], DS115[82], DS115[85], DS115[91], DS115[93], DS115[94], DS115[96], DS115[114], DS115[120], DS115[121], DS115[124], DS115[131], DS115[134], DS115[135], DS115[141], DS115[142], DS115[143], DS115[170], DS115[174], DS115[175], DS115[176], DS115[182], DS115[185], DS115[191], DS115[200], DS115[201], DS115[203], DS115[217], DS115[232], DS115[246], DS115[254], DS115[255], DS115[275], DS115[277], DS115[284], DS115[286], DS115[287], DS115[294], DS115[295], DS115[296], DS115[297], DS115[298], DS115[299], DS115[301], DS115[304], DS115[305], DS115[312], DS115[326], DS115[327], DS115[329], DS115[330], DS115[332], DS115[339], DS115[351], DS115[357], DS115[359], DS115[360], DS115[361], DS115[362], DS115[363], DS115[365], DS115[366], DS115[367], DS115[369], DS115[370], DS115[371], DS115[387], DS115[395], DS115[397], DS115[399], DS115[406], DS115[409], DS115[410], DS115[417], DS115[427], DS115[429], DS115[430], DS115[432], DS115[433], DS115[434], DS115[438], DS115[441], DS115[443], DS115[444], DS115[445], DS115[446], DS115[447], DS115[448], DS115[449], DS115[450], DS115[451], DS115[452], DS115[453], DS115[454], DS115[455], DS115[456], DS115[457], DS115[458], DS115[459], DS115[460], DS115[461], DS115[462], DS115[464], DS115[465], DS115[466], DS115[467], DS115[468], DS115[471], DS115[472], DS115[473], DS115[474], DS115[475], DS115[478], DS115[479], DS115[480], DS115[482], DS115[483], DS115[486], DS115[487], DS115[492], DS115[495], DS115[497], DS115[500], DS115[503], DS115[505], DS115[510], DS115[512], DS115[515], DS115[516], DS115[520], DS115[522], DS115[529], DS115[537], DS115[539], DS115[545], DS115[548], DS115[552], DS115[556], DS115[558], DS115[559], DS115[560], DS115[561], DS115[562], DS115[563], DS115[564], DS115[565], DS115[566], DS115[568], DS115[570], DS115[571], DS115[572], DS115[574], DS115[575], DS115[576], DS115[577], DS115[578], DS115[580], DS115[581], DS115[582], DS115[583], DS115[584], DS115[587], DS115[588], DS115[589], DS115[590], DS115[591], DS115[592], DS115[594], DS115[597], DS115[598], DS115[599], DS115[600], DS115[601], DS115[602], DS115[604], DS115[605], DS115[606], DS115[607], DS115[610], DS115[611], DS115[614], DS115[615], DS115[619], DS115[624], DS115[625], DS115[629], DS115[630], DS115[632], DS115[639], DS115[640], DS115[641], DS115[642], DS115[643], DS115[644], DS115[645], DS115[652], DS115[660], DS115[662], DS115[666], DS115[667], DS115[668], DS115[671], DS115[674], DS115[680], DS115[682], DS115[683], DS115[687], DS115[688], DS115[689], DS115[690], DS115[691], DS115[692], DS115[693], DS115[694], DS115[695], DS115[696], DS115[697], DS115[699], DS115[700], DS115[701], DS115[702], DS115[703], DS115[704], DS115[705], DS115[707], DS115[709], DS115[710], DS115[712], DS115[713], DS115[714], DS115[715], DS115[716], DS115[717], DS115[718], DS115[719], DS115[725], DS115[728], DS115[730], DS115[732], DS115[734], DS115[737], DS115[738], DS115[739], DS115[740], DS115[741], DS115[742], DS115[743], DS115[744], DS115[745], DS115[746], DS115[747], DS115[748], DS115[749], DS115[755], DS115[757], DS115[758], DS115[759], DS115[760], DS115[761], DS115[762], DS115[763], DS115[764], DS115[765], DS115[766], DS115[774], DS115[775], DS115[776], DS115[780], DS115[781], DS115[782], DS115[783], DS115[784], DS115[785], DS115[786], DS115[787], DS115[788], DS115[789], DS115[790], DS115[791], DS115[793], DS115[794], DS115[796], DS115[797], DS115[798], DS115[799], DS115[800], DS115[801], DS115[802], DS115[803], DS115[804], DS115[805], DS115[806], DS115[807], DS115[808], DS115[809], DS115[810], DS115[812], DS115[813], DS115[814], DS115[815], DS115[816], DS115[817], DS115[818], DS115[819], DS115[821], DS115[822], DS115[823], DS115[824], DS115[825], DS115[826], DS115[829], DS115[830], DS115[831], DS115[834], DS115[835], DS115[838], DS115[839], DS115[840], DS115[841], DS115[842], DS115[843], DS115[844], DS115[845], DS115[846], DS115[847], DS115[848], DS115[849], DS115[850], DS115[851], DS115[852], DS115[853], DS115[854], DS115[855], DS115[857], DS115[858], DS115[859], DS115[860], DS115[861], DS115[862], DS115[863], DS115[864], DS115[865], DS115[866], DS115[867], DS115[868], DS115[869], DS115[870], DS115[871], DS115[872], DS115[876], DS115[878], DS115[879], DS115[880], DS115[881], DS115[882], DS115[883], DS115[884], DS115[885], DS115[886], DS115[887], DS115[888], DS115[889], DS115[890], DS115[891], DS115[894], DS115[895], DS115[897], DS115[901], DS115[902], DS115[903], DS115[904], DS115[905], DS115[906], DS115[907], DS115[908], DS115[909], DS115[910], DS115[911], DS115[912], DS115[914], DS115[915], DS115[916], DS115[917], DS115[919], DS115[920], DS115[921], DS115[922], DS115[923], DS115[924], DS115[926], DS115[927], DS115[932], DS115[933], DS115[934], DS115[935], DS115[936], DS115[937], DS115[938], DS115[939], DS115[940], DS115[941], DS115[942], DS115[943], DS115[944], DS115[945], DS115[946], DS115[947], DS115[948], DS115[949], DS115[950], DS115[951], DS115[952], DS115[953], DS115[955], DS115[963], DS115[964], DS115[965], DS115[969], DS115[970], DS115[971], DS115[972], DS115[973], DS115[974], DS115[975], DS115[976], DS115[977], DS115[978], DS115[979], DS115[981], DS115[982], DS115[983], DS115[986], DS115[987], DS115[990], DS115[991], DS115[992], DS115[993], DS115[994], DS115[995], DS115[996], DS115[997], DS115[998], DS115[999], DS115[1000], DS115[1001], DS115[1002], DS115[1003], DS115[1004], DS115[1005], DS115[1006], DS115[1007], DS115[1008], DS115[1009], DS115[1010], DS115[1011], DS115[1012], DS115[1013], DS115[1014], DS115[1015], DS115[1016], DS115[1017], DS115[1018], DS115[1019], DS115[1021], DS115[1022], DS115[1023], DS115[1026], DS115[1027], DS115[1028], DS115[1029], DS115[1030], DS115[1033], DS115[1036], DS115[1037], DS115[1038], DS115[1039], DS115[1040], DS115[1041], DS115[1042], DS115[1043], DS115[1044], DS115[1045], DS115[1046], DS115[1047], DS115[1048], DS115[1049], DS115[1051], DS115[1053], DS115[1054], DS115[1055], DS115[1056], DS115[1057], DS115[1058], DS115[1061], DS115[1065], DS115[1067], DS115[1068], DS115[1070], DS115[1071], DS115[1072], DS115[1073], DS115[1074], DS115[1075], DS115[1076], DS115[1077], DS115[1078], DS115[1082], DS115[1084], DS115[1085], DS115[1086], DS115[1087], DS115[1088], DS115[1089], DS115[1090], DS115[1091], DS115[1093], DS115[1094], DS115[1095], DS115[1099], DS115[1100], DS115[1102], DS115[1104], DS115[1105], DS115[1106], DS115[1107], DS115[1108], DS115[1109], DS115[1110], DS115[1111], DS115[1112], DS115[1113], DS115[1114], DS115[1115], DS115[1116], DS115[1117], DS115[1118], DS115[1119], DS115[1120], DS115[1121], DS115[1122], DS115[1123], DS115[1124], DS115[1125], DS115[1126], DS115[1127], DS115[1128], DS115[1129], DS115[1133], DS115[1134], DS115[1135], DS115[1136], DS115[1137], DS115[1138], DS115[1139], DS115[1140], DS115[1141], DS115[1142], DS115[1143], DS115[1144], DS115[1145], DS115[1146], DS115[1147], DS115[1151], DS115[1153], DS115[1155], DS115[1156], DS115[1157], DS115[1158], DS115[1159], DS115[1160], DS115[1161], DS115[1162], DS115[1163], DS115[1164], DS115[1165], DS115[1166], DS115[1167], DS115[1168], DS115[1169], DS115[1170], DS115[1171], DS115[1172], DS115[1174], DS115[1175], DS115[1176], DS115[1177], DS115[1178], DS115[1179], DS115[1180], DS115[1181], DS115[1182], DS115[1183], DS115[1184], DS115[1185], DS115[1186], DS115[1187], DS115[1188], DS115[1189], DS115[1190], DS115[1191], DS115[1192], DS115[1193], DS115[1194], DS115[1196], DS115[1197], DS115[1198], DS115[1199], DS115[1200], DS115[1201], DS115[1202], DS115[1203], DS115[1204], DS115[1205], DS115[1206], DS115[1207], DS115[1208], DS115[1209], DS115[1210], DS115[1211], DS115[1212], DS115[1213], DS115[1214], DS115[1215], DS115[1216], DS115[1217], DS115[1219], DS115[1222], DS115[1224], DS115[1226], DS115[1227], DS115[1228], DS115[1229], DS115[1230], DS115[1231], DS115[1232], DS115[1233], DS115[1234], DS115[1235], DS115[1236], DS115[1237], DS115[1238], DS115[1239], DS115[1240], DS115[1241], DS115[1242], DS115[1243], DS115[1244], DS115[1245], DS115[1246], DS115[1247], DS115[1248], DS115[1249], DS115[1250], DS115[1251], DS115[1252], DS115[1253], DS115[1254], DS115[1255], DS115[1256], DS115[1257], DS115[1258], DS115[1259], DS115[1260], DS115[1261], DS115[1262], DS115[1263], DS115[1264], DS115[1265], DS115[1266], DS115[1267], DS115[1268], DS115[1269], DS115[1270], DS115[1271], DS115[1272], DS115[1273], DS115[1274], DS115[1275], DS115[1276], DS115[1277], DS115[1278], DS115[1279], DS115[1280], DS115[1281], DS115[1282], DS115[1283], DS115[1284], DS115[1285], DS115[1286], DS115[1287], DS115[1288], DS115[1289], DS115[1290], DS115[1291], DS115[1292], DS115[1293], DS115[1294], DS115[1295], DS115[1296], DS115[1297], DS115[1298], DS115[1299], DS115[1300], DS115[1301], DS115[1302], DS115[1303], DS115[1304], DS115[1305], DS115[1306], DS115[1307], DS115[1308], DS115[1309], DS115[1310], DS115[1311], DS115[1312], DS115[1313], DS115[1314], DS115[1315], DS115[1316], DS115[1317], DS115[1318], DS115[1319], DS115[1320], DS115[1321], DS115[1322], DS115[1323], DS115[1324], DS115[1325], DS115[1326], DS115[1327], DS115[1328], DS115[1329], DS115[1330], DS115[1331], DS115[1332], DS115[1333], DS115[1334], DS115[1335], DS115[1336], DS115[1337], DS115[1338], DS115[1339], DS115[1340], DS115[1341], DS115[1342], DS115[1343], DS115[1344], DS115[1345], DS115[1346], DS115[1347], DS115[1348], DS115[1349], DS115[1350], DS115[1351], DS115[1352], DS115[1353], DS115[1354], DS115[1355], DS115[1356], DS115[1357], DS115[1358], DS115[1359], DS115[1360], DS115[1361], DS115[1362], DS115[1363], DS115[1364], DS115[1365], DS115[1366], DS115[1367], DS115[1368], DS115[1369], DS115[1370], DS115[1371], DS115[1372], DS115[1373], DS115[1374], DS115[1375], DS115[1376], DS115[1377], DS115[1378], DS115[1379], DS115[1380], DS115[1381], DS115[1382], DS115[1383], DS115[1384], DS115[1385], DS115[1386], DS115[1387], DS115[1388], DS115[1389], DS115[1390], DS115[1391], DS115[1392], DS115[1393], DS115[1394], DS115[1395], DS115[1396], DS115[1397], DS115[1398], DS115[1399], DS115[1400], DS115[1401], DS115[1402], DS115[1403], DS115[1404], DS115[1405], DS115[1406], DS115[1407], DS115[1408], DS115[1409], DS115[1412], DS115[1413], DS115[1414], DS115[1415], DS115[1418], DS115[1419], DS115[1420], DS115[1421], DS115[1422], DS115[1424], DS115[1425], DS115[1426], DS115[1427], DS115[1428], DS115[1429], DS115[1430], DS115[1431], DS115[1432], DS115[1433], DS115[1434], DS115[1437], DS115[1438], DS115[1447], DS115[1448], DS115[1449], DS115[1451], DS115[1452], DS115[1454], DS115[1455], DS115[1456], DS115[1457], DS115[1458], DS115[1459], DS115[1460], DS115[1461], DS115[1462], DS115[1463], DS115[1465], DS115[1466], DS115[1467], DS115[1468], DS115[1469], DS115[1470], DS115[1471], DS115[1472], DS115[1473], DS115[1474], DS115[1475], DS115[1478], DS115[1479], DS115[1480], DS115[1481], DS115[1482], DS115[1483], DS115[1484], DS115[1485], DS115[1486], DS115[1487], DS115[1488], DS115[1489], DS115[1490], DS115[1491], DS115[1492], DS115[1493], DS115[1494], DS115[1495], DS115[1496], DS115[1497], DS115[1498], DS115[1499], DS115[1500], DS115[1501], DS115[1502], DS115[1503], DS115[1504], DS115[1505], DS115[1506], DS115[1507], DS115[1508], DS115[1509], DS115[1510], DS115[1511], DS115[1512], DS115[1513], DS115[1514], DS115[1515], DS115[1519], DS115[1520], DS115[1521], DS115[1522], DS115[1523], DS115[1524], DS115[1525], DS115[1526], DS115[1527], DS115[1528], DS115[1529], DS115[1530], DS115[1531], DS115[1532], DS115[1533], DS115[1534], DS115[1535], DS115[1536], DS115[1537], DS115[1538], DS115[1539], DS115[1540], DS115[1541], DS115[1542], DS115[1543], DS115[1544], DS115[1545], DS115[1546], DS115[1547], DS115[1548], DS115[1549], DS115[1550], DS115[1551], DS115[1552], DS115[1553], DS115[1554], DS115[1555], DS115[1556], DS115[1557], DS115[1558], DS115[1559], DS115[1560], DS115[1561], DS115[1562], DS115[1563], DS115[1564], DS115[1565], DS115[1566], DS115[1567], DS115[1568], DS115[1569], DS115[1570], DS115[1571], DS115[1572], DS115[1573], DS115[1574], DS115[1575], DS115[1576], DS115[1577], DS115[1578], DS115[1579], DS115[1580], DS115[1581], DS115[1582], DS115[1583], DS115[1584], DS115[1585], DS115[1586], DS115[1587], DS115[1588], DS115[1589], DS115[1590], DS115[1591], DS115[1592], DS115[1593], DS115[1594], DS115[1595], DS115[1596], DS115[1597], DS115[1598], DS115[1599], DS115[1600], DS115[1601], DS115[1602], DS115[1603], DS115[1604], DS115[1605], DS115[1606], DS115[1607], DS115[1608], DS115[1609], DS115[1610], DS115[1611], DS115[1612], DS115[1613], DS115[1614], DS115[1615], DS115[1616], DS115[1617], DS115[1618], DS115[1619], DS115[1620], DS115[1621], DS115[1622], DS115[1623], DS115[1624]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,115]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,115] is 6 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,115] is RDS115:=[ [ 2, 3, 4, 7, 8, 13, 14, 18, 19, 21, 23, 26, 28, 30, 31, 32, 41, 43, 44, 45, 46, 49, 53, 54, 55, 58, 59, 61 ], [ 2, 3, 4, 7, 8, 9, 13, 14, 18, 19, 21, 26, 27, 28, 29, 30, 31, 32, 41, 44, 46, 49, 50, 53, 54, 55, 58, 61 ], [ 2, 3, 4, 6, 7, 8, 13, 14, 18, 19, 20, 21, 22, 26, 28, 30, 31, 32, 41, 42, 44, 46, 49, 53, 54, 55, 58, 61 ], [ 1, 2, 3, 4, 5, 8, 13, 14, 18, 19, 23, 26, 28, 30, 31, 32, 41, 43, 45, 46, 49, 53, 54, 55, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 14, 18, 19, 26, 27, 28, 29, 30, 31, 32, 41, 46, 49, 50, 53, 54, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 18, 19, 20, 22, 26, 28, 30, 31, 32, 41, 42, 46, 49, 53, 54, 55, 60, 61, 64 ] ]; ########################### ########################### ###########################