### 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 [64,119]. 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 [64,119]. # 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(64,119));' can be # used to create a list e of the elements of the group [64,119]. # In our list of (64,28,12) DSs in group [64,119], we have [1, # 2, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 24, 25, 28, # 30, 31, 32, 33, 35, 38, 39, 42, 46, 50, 54, 57, 62]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[8], e[9], e[13], e[15], e[16], e[19], e[22], e[24], e[25], e[28], e[30], # e[31], e[32], e[33], e[35], e[38], e[39], e[42], e[46], e[50], e[54], e[57], e[62]] # where e is the list of the elements of the group [64,119] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,119));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 119] ### The number of inequivalent (64,28,12) DSs in group [64,119] is 2024 ### The list of all inequivalent (64,28,12) DSs in group [64,119] is DS119:=[ [ 1, 2, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 24, 25, 28, 30, 31, 32, 33, 35, 38, 39, 42, 46, 50, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 24, 25, 27, 28, 30, 31, 32, 33, 35, 38, 39, 42, 46, 49, 54, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 15, 16, 17, 22, 24, 25, 28, 30, 33, 35, 38, 41, 42, 46, 50, 52, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 15, 16, 17, 22, 24, 25, 27, 28, 30, 33, 35, 38, 41, 42, 46, 49, 52, 54, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 14, 18, 19, 22, 25, 28, 30, 33, 35, 38, 41, 42, 47, 50, 52, 54, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 14, 18, 19, 22, 25, 27, 28, 30, 33, 35, 38, 41, 42, 47, 49, 52, 54, 56, 61 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 14, 18, 19, 22, 24, 25, 28, 30, 33, 35, 38, 41, 42, 46, 50, 52, 54, 56, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 14, 18, 19, 22, 24, 25, 27, 28, 30, 33, 35, 38, 41, 42, 46, 49, 52, 54, 56 ], [ 1, 2, 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54, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 20, 21, 29, 33, 34, 37, 38, 45, 50, 51, 54, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 21, 29, 34, 42, 46, 51, 53, 54, 56, 57, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 31, 36, 41, 44, 52, 53, 54, 55, 57, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 27, 36, 37, 41, 44, 49, 53, 55, 56, 57, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 27, 30, 31, 33, 40, 41, 44, 53, 54, 55, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 27, 30, 31, 33, 40, 41, 43, 44, 46, 53, 54, 55, 56 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 31, 34, 35, 36, 40, 41, 44, 50, 52, 54, 55, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 31, 34, 35, 36, 40, 41, 43, 44, 46, 50, 52, 54, 55, 56 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 30, 34, 35, 37, 40, 41, 44, 49, 52, 53, 55, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 30, 34, 35, 37, 40, 41, 43, 44, 46, 49, 52, 53, 55, 56 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 30, 34, 35, 36, 37, 40, 41, 44, 49, 52, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 30, 34, 35, 36, 37, 40, 41, 43, 44, 46, 49, 52, 55, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 27, 30, 31, 34, 35, 36, 40, 41, 44, 54, 55, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 27, 30, 31, 34, 35, 36, 40, 41, 43, 44, 46, 54, 55, 56 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 30, 34, 38, 40, 41, 44, 49, 52, 53, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 30, 34, 38, 40, 41, 43, 44, 46, 49, 52, 53, 54, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 27, 34, 36, 38, 40, 41, 44, 49, 50, 54, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 27, 34, 36, 38, 40, 41, 43, 44, 46, 49, 50, 54, 56 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 29, 35, 36, 38, 39, 40, 45, 50, 51, 53, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 29, 35, 36, 38, 39, 40, 45, 46, 50, 51, 53, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 21, 29, 33, 34, 38, 40, 42, 45, 46, 50, 51, 53, 54, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 31, 35, 38, 40, 41, 44, 50, 52, 53, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 31, 35, 38, 40, 41, 43, 44, 46, 50, 52, 53, 54, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 27, 35, 37, 38, 40, 41, 44, 49, 50, 53, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 27, 35, 37, 38, 40, 41, 43, 44, 46, 49, 50, 53, 56 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 27, 35, 36, 37, 38, 40, 41, 44, 49, 50, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 27, 35, 36, 37, 38, 40, 41, 43, 44, 46, 49, 50, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 27, 30, 31, 35, 38, 40, 41, 44, 53, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 27, 30, 31, 35, 38, 40, 41, 43, 44, 46, 53, 54, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 29, 34, 37, 38, 39, 40, 45, 50, 51, 54, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 29, 34, 37, 38, 39, 40, 45, 46, 50, 51, 54, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 29, 33, 34, 36, 37, 38, 39, 40, 45, 50, 51, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 29, 33, 34, 36, 37, 38, 39, 40, 45, 46, 50, 51, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 20, 21, 29, 33, 34, 38, 45, 50, 51, 53, 54, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 29, 34, 36, 39, 46, 51, 53, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 21, 29, 34, 35, 36, 37, 40, 42, 45, 50, 51, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 21, 29, 34, 35, 36, 37, 40, 42, 45, 46, 50, 51, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 21, 25, 26, 29, 33, 36, 42, 43, 45, 51, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 25, 29, 33, 36, 39, 43, 45, 47, 48, 51, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 29, 34, 35, 39, 40, 45, 50, 51, 53, 54, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 29, 34, 35, 39, 40, 45, 46, 50, 51, 53, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 29, 33, 34, 35, 36, 39, 40, 45, 50, 51, 53, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 29, 33, 34, 35, 36, 39, 40, 45, 46, 50, 51, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 24, 25, 26, 29, 33, 36, 39, 45, 46, 51, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 20, 21, 29, 34, 35, 36, 37, 45, 50, 51, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 20, 21, 29, 33, 37, 38, 39, 45, 46, 51, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 21, 29, 33, 36, 42, 43, 45, 51, 53, 54, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 29, 36, 37, 39, 43, 45, 51, 54, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20, 21, 29, 45, 46, 50, 51, 53, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20, 21, 29, 33, 36, 45, 46, 50, 51, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 29, 34, 35, 36, 40, 42, 45, 50, 51, 53, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 29, 34, 35, 36, 40, 42, 45, 46, 50, 51, 53, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 20, 21, 29, 34, 35, 36, 45, 50, 51, 53, 56, 58, 61 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1010 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS119[3], DS119[6], DS119[10], DS119[18], DS119[19], DS119[22], DS119[26], DS119[36], DS119[37], DS119[38], DS119[39], DS119[40], DS119[41], DS119[45], DS119[46], DS119[48], DS119[50], DS119[53], DS119[55], DS119[58], DS119[61], DS119[63], DS119[65], DS119[67], DS119[69], DS119[77], DS119[78], DS119[81], DS119[89], DS119[91], DS119[92], DS119[97], DS119[101], DS119[102], DS119[103], DS119[104], DS119[109], DS119[110], DS119[111], DS119[112], DS119[113], DS119[115], DS119[123], DS119[124], DS119[127], DS119[131], DS119[136], DS119[137], DS119[141], DS119[144], DS119[148], DS119[152], DS119[153], DS119[154], DS119[157], DS119[158], DS119[162], DS119[187], DS119[190], DS119[194], DS119[197], DS119[204], DS119[211], DS119[212], DS119[217], DS119[222], DS119[224], DS119[225], DS119[227], DS119[231], DS119[234], DS119[237], DS119[243], DS119[246], DS119[247], DS119[260], DS119[265], DS119[266], DS119[268], DS119[270], DS119[274], DS119[275], DS119[280], DS119[284], DS119[289], DS119[290], DS119[291], DS119[292], DS119[293], DS119[296], DS119[302], DS119[304], DS119[307], DS119[308], DS119[309], DS119[310], DS119[312], DS119[316], DS119[317], DS119[330], DS119[333], DS119[342], DS119[344], DS119[345], DS119[346], DS119[349], DS119[350], DS119[352], DS119[353], DS119[354], DS119[355], DS119[357], DS119[358], DS119[359], DS119[361], DS119[362], DS119[364], DS119[366], DS119[367], DS119[370], DS119[371], DS119[372], DS119[373], DS119[374], DS119[375], DS119[376], DS119[378], DS119[383], DS119[394], DS119[397], DS119[401], DS119[404], DS119[406], DS119[407], DS119[408], DS119[413], DS119[416], DS119[421], DS119[426], DS119[428], DS119[435], DS119[436], DS119[438], DS119[440], DS119[446], DS119[454], DS119[455], DS119[457], DS119[458], DS119[459], DS119[464], DS119[466], DS119[468], DS119[471], DS119[480], DS119[482], DS119[488], DS119[489], DS119[494], DS119[497], DS119[505], DS119[509], DS119[514], DS119[519], DS119[520], DS119[523], DS119[529], DS119[533], DS119[534], DS119[543], DS119[545], DS119[559], DS119[563], DS119[566], DS119[569], DS119[570], DS119[574], DS119[575], DS119[576], DS119[579], DS119[580], DS119[584], DS119[585], DS119[586], DS119[602], DS119[603], DS119[604], DS119[611], DS119[613], DS119[620], DS119[622], DS119[623], DS119[624], DS119[625], DS119[628], DS119[637], DS119[641], DS119[642], DS119[645], DS119[648], DS119[650], DS119[651], DS119[656], DS119[658], DS119[660], DS119[662], DS119[663], DS119[667], DS119[669], DS119[670], DS119[672], DS119[677], DS119[681], DS119[688], DS119[693], DS119[701], DS119[710], DS119[714], DS119[715], DS119[716], DS119[727], DS119[728], DS119[734], DS119[735], DS119[736], DS119[738], DS119[740], DS119[745], DS119[752], DS119[755], DS119[758], DS119[759], DS119[760], DS119[761], DS119[763], DS119[772], DS119[775], DS119[778], DS119[779], DS119[787], DS119[788], DS119[792], DS119[794], DS119[795], DS119[798], DS119[799], DS119[800], DS119[801], DS119[802], DS119[804], DS119[824], DS119[830], DS119[831], DS119[832], DS119[835], DS119[836], DS119[837], DS119[838], DS119[843], DS119[845], DS119[846], DS119[851], DS119[852], DS119[856], DS119[858], DS119[859], DS119[862], DS119[863], DS119[864], DS119[865], DS119[866], DS119[867], DS119[868], DS119[870], DS119[872], DS119[876], DS119[878], DS119[881], DS119[883], DS119[884], DS119[885], DS119[886], DS119[898], DS119[903], DS119[912], DS119[913], DS119[914], DS119[918], DS119[924], DS119[925], DS119[926], DS119[927], DS119[928], DS119[929], DS119[930], DS119[932], DS119[933], DS119[934], DS119[935], DS119[939], DS119[940], DS119[941], DS119[942], DS119[943], DS119[945], DS119[946], DS119[949], DS119[950], DS119[953], DS119[955], DS119[959], DS119[960], DS119[961], DS119[963], DS119[964], DS119[966], DS119[969], DS119[971], DS119[972], DS119[980], DS119[982], DS119[983], DS119[985], DS119[989], DS119[990], DS119[991], DS119[992], DS119[993], DS119[994], DS119[998], DS119[999], DS119[1001], DS119[1002], DS119[1004], DS119[1007], DS119[1009], DS119[1010], DS119[1011], DS119[1016], DS119[1017], DS119[1018], DS119[1019], DS119[1022], DS119[1024], DS119[1025], DS119[1028], DS119[1029], DS119[1030], DS119[1032], DS119[1033], DS119[1036], DS119[1038], DS119[1039], DS119[1042], DS119[1045], DS119[1046], DS119[1049], DS119[1056], DS119[1058], DS119[1061], DS119[1062], DS119[1063], DS119[1065], DS119[1070], DS119[1071], DS119[1072], DS119[1077], DS119[1078], DS119[1086], DS119[1090], DS119[1093], DS119[1096], DS119[1097], DS119[1098], DS119[1099], DS119[1103], DS119[1107], DS119[1108], DS119[1109], DS119[1111], DS119[1112], DS119[1113], DS119[1119], DS119[1120], DS119[1125], DS119[1126], DS119[1127], DS119[1130], DS119[1133], DS119[1137], DS119[1140], DS119[1144], DS119[1145], DS119[1146], DS119[1147], DS119[1148], DS119[1149], DS119[1150], DS119[1153], DS119[1154], DS119[1155], DS119[1156], DS119[1158], DS119[1159], DS119[1160], DS119[1163], DS119[1164], DS119[1165], DS119[1166], DS119[1167], DS119[1168], DS119[1170], DS119[1171], DS119[1172], DS119[1173], DS119[1177], DS119[1178], DS119[1179], DS119[1180], DS119[1181], DS119[1185], DS119[1186], DS119[1187], DS119[1191], DS119[1192], DS119[1194], DS119[1199], DS119[1201], DS119[1210], DS119[1211], DS119[1212], DS119[1213], DS119[1214], DS119[1216], DS119[1217], DS119[1218], DS119[1219], DS119[1220], DS119[1221], DS119[1223], DS119[1224], DS119[1226], DS119[1228], DS119[1229], DS119[1230], DS119[1232], DS119[1233], DS119[1234], DS119[1235], DS119[1240], DS119[1242], DS119[1243], DS119[1244], DS119[1245], DS119[1246], DS119[1247], DS119[1252], DS119[1253], DS119[1254], DS119[1255], DS119[1257], DS119[1258], DS119[1259], DS119[1262], DS119[1265], DS119[1266], DS119[1267], DS119[1269], DS119[1270], DS119[1272], DS119[1277], DS119[1278], DS119[1283], DS119[1284], DS119[1285], DS119[1288], DS119[1289], DS119[1291], DS119[1301], DS119[1303], DS119[1304], DS119[1306], DS119[1307], DS119[1309], DS119[1310], DS119[1311], DS119[1312], DS119[1313], DS119[1314], DS119[1315], DS119[1316], DS119[1317], DS119[1319], DS119[1321], DS119[1323], DS119[1324], DS119[1328], DS119[1329], DS119[1333], DS119[1337], DS119[1338], DS119[1341], DS119[1342], DS119[1343], DS119[1344], DS119[1345], DS119[1346], DS119[1347], DS119[1348], DS119[1349], DS119[1350], DS119[1351], DS119[1352], DS119[1353], DS119[1354], DS119[1355], DS119[1360], DS119[1361], DS119[1363], DS119[1365], DS119[1366], DS119[1367], DS119[1368], DS119[1369], DS119[1372], DS119[1376], DS119[1379], DS119[1384], DS119[1385], DS119[1387], DS119[1389], DS119[1390], DS119[1391], DS119[1392], DS119[1393], DS119[1394], DS119[1395], DS119[1396], DS119[1397], DS119[1398], DS119[1403], DS119[1404], DS119[1405], DS119[1406], DS119[1407], DS119[1408], DS119[1409], DS119[1410], DS119[1411], DS119[1412], DS119[1413], DS119[1414], DS119[1415], DS119[1416], DS119[1417], DS119[1418], DS119[1419], DS119[1420], DS119[1421], DS119[1422], DS119[1423], DS119[1424], DS119[1425], DS119[1426], DS119[1427], DS119[1428], DS119[1429], DS119[1430], DS119[1431], DS119[1432], DS119[1433], DS119[1434], DS119[1435], DS119[1436], DS119[1437], DS119[1438], DS119[1439], DS119[1440], DS119[1441], DS119[1442], DS119[1443], DS119[1444], DS119[1445], DS119[1446], DS119[1447], DS119[1448], DS119[1449], DS119[1450], DS119[1451], DS119[1452], DS119[1453], DS119[1454], DS119[1455], DS119[1456], DS119[1457], DS119[1458], DS119[1459], DS119[1460], DS119[1461], DS119[1462], DS119[1463], DS119[1464], DS119[1465], DS119[1466], DS119[1467], DS119[1468], DS119[1469], DS119[1470], DS119[1471], DS119[1472], DS119[1473], DS119[1474], DS119[1475], DS119[1476], DS119[1477], DS119[1478], DS119[1479], DS119[1480], DS119[1481], DS119[1482], DS119[1483], DS119[1484], DS119[1485], DS119[1486], DS119[1487], DS119[1488], DS119[1489], DS119[1490], DS119[1491], DS119[1492], DS119[1493], DS119[1494], DS119[1495], DS119[1496], DS119[1497], DS119[1498], DS119[1499], DS119[1500], DS119[1501], DS119[1502], DS119[1503], DS119[1504], DS119[1505], DS119[1506], DS119[1507], DS119[1508], DS119[1509], DS119[1510], DS119[1511], DS119[1512], DS119[1513], DS119[1514], DS119[1515], DS119[1516], DS119[1517], DS119[1518], DS119[1519], DS119[1520], DS119[1521], DS119[1522], DS119[1523], DS119[1524], DS119[1525], DS119[1528], DS119[1535], DS119[1540], DS119[1551], DS119[1561], DS119[1562], DS119[1563], DS119[1564], DS119[1565], DS119[1566], DS119[1567], DS119[1568], DS119[1587], DS119[1589], DS119[1590], DS119[1592], DS119[1593], DS119[1594], DS119[1595], DS119[1596], DS119[1597], DS119[1598], DS119[1599], DS119[1600], DS119[1601], DS119[1602], DS119[1603], DS119[1604], DS119[1605], DS119[1606], DS119[1608], DS119[1609], DS119[1610], DS119[1611], DS119[1622], DS119[1627], DS119[1628], DS119[1629], DS119[1630], DS119[1631], DS119[1632], DS119[1633], DS119[1634], DS119[1635], DS119[1636], DS119[1637], DS119[1638], DS119[1639], DS119[1640], DS119[1641], DS119[1642], DS119[1643], DS119[1644], DS119[1645], DS119[1646], DS119[1647], DS119[1648], DS119[1649], DS119[1650], DS119[1651], DS119[1652], DS119[1653], DS119[1654], DS119[1655], DS119[1656], DS119[1657], DS119[1658], DS119[1659], DS119[1660], DS119[1661], DS119[1662], DS119[1663], DS119[1664], DS119[1665], DS119[1666], DS119[1667], DS119[1668], DS119[1669], DS119[1670], DS119[1671], DS119[1672], DS119[1673], DS119[1674], DS119[1675], DS119[1676], DS119[1677], DS119[1678], DS119[1679], DS119[1680], DS119[1681], DS119[1682], DS119[1683], DS119[1684], DS119[1685], DS119[1686], DS119[1687], DS119[1688], DS119[1689], DS119[1690], DS119[1691], DS119[1692], DS119[1693], DS119[1694], DS119[1695], DS119[1696], DS119[1697], DS119[1698], DS119[1699], DS119[1700], DS119[1701], DS119[1702], DS119[1703], DS119[1704], DS119[1705], DS119[1706], DS119[1707], DS119[1708], DS119[1709], DS119[1710], DS119[1711], DS119[1712], DS119[1722], DS119[1741], DS119[1743], DS119[1746], DS119[1747], DS119[1748], DS119[1749], DS119[1750], DS119[1751], DS119[1752], DS119[1753], DS119[1754], DS119[1755], DS119[1756], DS119[1757], DS119[1758], DS119[1759], DS119[1760], DS119[1761], DS119[1762], DS119[1763], DS119[1764], DS119[1765], DS119[1766], DS119[1767], DS119[1768], DS119[1769], DS119[1770], DS119[1771], DS119[1772], DS119[1773], DS119[1774], DS119[1776], DS119[1777], DS119[1778], DS119[1779], DS119[1782], DS119[1784], DS119[1785], DS119[1786], DS119[1787], DS119[1788], DS119[1791], DS119[1792], DS119[1793], DS119[1794], DS119[1795], DS119[1796], DS119[1797], DS119[1798], DS119[1799], DS119[1800], DS119[1801], DS119[1802], DS119[1803], DS119[1805], DS119[1808], DS119[1811], DS119[1812], DS119[1813], DS119[1814], DS119[1816], DS119[1820], DS119[1823], DS119[1826], DS119[1827], DS119[1833], DS119[1840], DS119[1841], DS119[1842], DS119[1843], DS119[1845], DS119[1846], DS119[1847], DS119[1848], DS119[1849], DS119[1850], DS119[1851], DS119[1852], DS119[1853], DS119[1854], DS119[1855], DS119[1856], DS119[1857], DS119[1858], DS119[1859], DS119[1860], DS119[1861], DS119[1862], DS119[1863], DS119[1864], DS119[1865], DS119[1866], DS119[1867], DS119[1868], DS119[1869], DS119[1870], DS119[1871], DS119[1872], DS119[1873], DS119[1875], DS119[1876], DS119[1877], DS119[1878], DS119[1879], DS119[1880], DS119[1881], DS119[1882], DS119[1883], DS119[1884], DS119[1885], DS119[1886], DS119[1887], DS119[1890], DS119[1891], DS119[1892], DS119[1894], DS119[1896], DS119[1903], DS119[1907], DS119[1910], DS119[1914], DS119[1915], DS119[1916], DS119[1917], DS119[1918], DS119[1919], DS119[1920], DS119[1921], DS119[1922], DS119[1923], DS119[1924], DS119[1925], DS119[1926], DS119[1927], DS119[1929], DS119[1930], DS119[1933], DS119[1934], DS119[1935], DS119[1937], DS119[1938], DS119[1939], DS119[1940], DS119[1941], DS119[1942], DS119[1944], DS119[1945], DS119[1946], DS119[1947], DS119[1949], DS119[1950], DS119[1951], DS119[1952], DS119[1953], DS119[1954], DS119[1955], DS119[1956], DS119[1957], DS119[1958], DS119[1959], DS119[1960], DS119[1961], DS119[1962], DS119[1963], DS119[1964], DS119[1965], DS119[1966], DS119[1967], DS119[1968], DS119[1969], DS119[1970], DS119[1971], DS119[1972], DS119[1973], DS119[1974], DS119[1975], DS119[1976], DS119[1977], DS119[1978], DS119[1979], DS119[1980], DS119[1981], DS119[1982], DS119[1983], DS119[1984], DS119[1985], DS119[1986], DS119[1987], DS119[1988], DS119[1989], DS119[1990], DS119[1991], DS119[1992], DS119[1993], DS119[1994], DS119[1995], DS119[1996], DS119[1997], DS119[1998], DS119[1999], DS119[2000], DS119[2001], DS119[2002], DS119[2003], DS119[2004], DS119[2005], DS119[2006], DS119[2007], DS119[2008], DS119[2009], DS119[2010], DS119[2011], DS119[2012], DS119[2013], DS119[2014], DS119[2015], DS119[2016], DS119[2017], DS119[2018], DS119[2019], DS119[2020], DS119[2021], DS119[2022], DS119[2023], DS119[2024]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,119]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,119] is 152 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,119] is RDS119:=[ [ 3, 6, 8, 9, 13, 16, 17, 20, 22, 23, 25, 27, 28, 33, 36, 39, 40, 42, 47, 49, 55, 56, 57, 58, 59, 60, 61, 63 ], [ 3, 5, 6, 8, 9, 13, 14, 16, 17, 21, 22, 23, 25, 27, 28, 33, 37, 39, 40, 47, 49, 55, 57, 58, 59, 60, 61, 63 ], [ 3, 4, 6, 8, 9, 13, 16, 18, 19, 20, 22, 23, 25, 27, 28, 33, 36, 41, 42, 47, 49, 55, 56, 58, 59, 60, 61, 63 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 16, 18, 19, 21, 22, 23, 25, 27, 28, 33, 37, 41, 47, 49, 55, 58, 59, 60, 61, 63 ], [ 2, 6, 8, 9, 10, 11, 13, 17, 20, 22, 23, 26, 28, 30, 33, 39, 40, 42, 46, 50, 55, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 6, 8, 9, 10, 11, 13, 17, 20, 22, 23, 25, 29, 30, 33, 39, 40, 42, 47, 49, 55, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 5, 6, 8, 9, 10, 11, 13, 17, 21, 22, 23, 25, 27, 29, 30, 33, 39, 40, 47, 50, 55, 57, 58, 59, 60, 61, 63 ], [ 2, 4, 6, 8, 9, 10, 11, 13, 18, 19, 20, 22, 23, 26, 28, 30, 33, 41, 42, 46, 50, 55, 58, 59, 60, 61, 62, 63 ], [ 2, 4, 6, 8, 9, 10, 11, 13, 18, 19, 20, 22, 23, 25, 29, 30, 33, 41, 42, 47, 49, 55, 58, 59, 60, 61, 62, 63 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 18, 19, 21, 22, 23, 25, 27, 29, 30, 33, 41, 47, 50, 55, 58, 59, 60, 61, 63 ], [ 2, 3, 8, 9, 10, 11, 13, 16, 17, 23, 25, 27, 29, 30, 33, 36, 39, 40, 47, 50, 55, 56, 57, 58, 59, 60, 61, 63 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 26, 28, 30, 37, 39, 40, 46, 50, 53, 54, 55, 57, 58, 59, 60, 61, 62 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 26, 28, 30, 33, 37, 39, 40, 46, 50, 55, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 25, 29, 30, 33, 37, 39, 40, 47, 49, 55, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 3, 6, 9, 10, 11, 13, 16, 17, 20, 22, 23, 28, 30, 33, 36, 39, 40, 42, 50, 55, 56, 57, 58, 59, 60, 62, 63 ], [ 2, 3, 6, 8, 10, 11, 13, 16, 17, 20, 22, 23, 25, 30, 33, 36, 39, 40, 42, 47, 55, 56, 57, 58, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 11, 13, 15, 16, 20, 22, 23, 26, 27, 28, 31, 33, 38, 42, 46, 49, 52, 55, 58, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 11, 13, 15, 16, 20, 22, 23, 25, 29, 31, 33, 38, 42, 47, 49, 52, 55, 58, 59, 60, 61, 62, 63 ], [ 2, 3, 6, 8, 9, 11, 12, 13, 16, 20, 22, 23, 25, 27, 28, 32, 36, 42, 47, 49, 53, 54, 55, 56, 58, 59, 60, 61 ], [ 2, 3, 6, 8, 9, 11, 12, 13, 16, 20, 22, 23, 25, 27, 28, 32, 33, 36, 42, 47, 49, 55, 56, 58, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 20, 22, 25, 27, 30, 33, 36, 42, 43, 44, 45, 47, 51, 53, 54, 56, 61, 62, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 20, 22, 23, 25, 30, 33, 36, 42, 47, 49, 50, 51, 53, 54, 56, 58, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 20, 22, 23, 25, 27, 30, 33, 36, 42, 47, 51, 53, 54, 56, 58, 59, 60, 61, 62, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 25, 27, 30, 36, 39, 40, 42, 43, 44, 45, 47, 51, 56, 57, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 23, 25, 30, 36, 39, 40, 42, 47, 49, 50, 51, 56, 57, 58, 59, 60, 61 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 23, 25, 27, 30, 36, 39, 40, 42, 47, 51, 56, 57, 58, 59, 60, 61, 62 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 16, 20, 22, 25, 27, 30, 34, 35, 36, 42, 43, 44, 45, 47, 51, 55, 56, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 16, 20, 22, 23, 25, 30, 34, 35, 36, 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