### 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 [64,114]. 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 [64,114]. # 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(64,114));' can be # used to create a list e of the elements of the group [64,114]. # In our list of (64,28,12) DSs in group [64,114], we have [1, # 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 19, 22, 23, 28, # 31, 34, 38, 39, 43, 44, 49, 50, 54, 56, 57, 63, 64]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[6], e[7], e[9], e[10], e[12], e[13], e[14], e[19], e[22], e[23], e[28], e[31], # e[34], e[38], e[39], e[43], e[44], e[49], e[50], e[54], e[56], e[57], e[63], e[64]] # where e is the list of the elements of the group [64,114] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,114));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 114] ### The number of inequivalent (64,28,12) DSs in group [64,114] is 1244 ### The list of all inequivalent (64,28,12) DSs in group [64,114] is DS114:=[ [ 1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 19, 22, 23, 28, 31, 34, 38, 39, 43, 44, 49, 50, 54, 56, 57, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 15, 19, 22, 24, 25, 27, 29, 30, 31, 33, 37, 39, 50, 55, 56, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 14, 15, 18, 22, 28, 29, 31, 36, 40, 42, 43, 44, 51, 53, 54, 55, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 14, 15, 18, 22, 23, 28, 29, 31, 36, 40, 42, 45, 51, 53, 54, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 21, 26, 28, 29, 30, 37, 39, 40, 41, 45, 46, 51, 56, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 21, 25, 26, 29, 30, 37, 39, 40, 41, 45, 48, 49, 56, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 21, 23, 26, 28, 29, 30, 37, 39, 40, 41, 43, 44, 46, 51, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 21, 23, 25, 26, 29, 30, 37, 39, 40, 41, 43, 44, 48, 49, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 16, 19, 21, 23, 25, 30, 38, 39, 43, 44, 47, 49, 50, 51, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 16, 17, 20, 23, 25, 31, 34, 35, 36, 41, 46, 48, 52, 55, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 15, 16, 19, 20, 28, 31, 33, 34, 38, 39, 43, 44, 45, 49, 51, 52, 53, 57, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 15, 16, 19, 20, 25, 31, 33, 34, 38, 39, 43, 44, 45, 46, 48, 52, 53, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 15, 16, 19, 20, 23, 28, 31, 33, 34, 38, 39, 49, 51, 52, 53, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 15, 16, 19, 20, 23, 25, 31, 33, 34, 38, 39, 46, 48, 52, 53, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 15, 16, 17, 20, 23, 25, 31, 35, 38, 41, 46, 48, 52, 53, 57, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 14, 19, 20, 23, 28, 31, 34, 35, 38, 39, 49, 51, 52, 55, 56, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 11, 13, 14, 18, 19, 20, 23, 28, 31, 35, 38, 41, 49, 51, 52, 53, 56, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 11, 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48, 51, 53, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 20, 22, 26, 29, 34, 37, 38, 45, 49, 51, 52, 53, 55, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 20, 22, 26, 28, 29, 34, 37, 38, 43, 45, 49, 52, 53, 55, 57 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 28, 31, 36, 37, 38, 40, 41, 45, 49, 55, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 20, 22, 31, 37, 40, 41, 44, 45, 49, 55, 56, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 29, 31, 36, 37, 38, 39, 41, 45, 50, 55, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 29, 30, 31, 32, 37, 44, 45, 50, 55, 56, 58, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 20, 22, 29, 31, 34, 37, 45, 50, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 20, 22, 26, 29, 34, 45, 49, 51, 52, 53, 55, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 20, 22, 23, 26, 28, 29, 34, 49, 52, 53, 55, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 21, 22, 28, 31, 34, 35, 40, 48, 51, 53, 56, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 21, 22, 23, 28, 31, 35, 40, 48, 51, 55, 56, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 26, 27, 29, 33, 36, 42, 44, 47, 48, 51, 55, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 20, 21, 33, 35, 36, 37, 43, 49, 51, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 20, 21, 33, 34, 35, 36, 37, 45, 49, 51, 53, 56, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 20, 21, 25, 33, 35, 37, 39, 43, 48, 51, 55, 57, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 19, 20, 26, 34, 36, 42, 43, 47, 48, 51, 53, 54, 55, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 27, 29, 30, 33, 37, 38, 41, 44, 46, 52, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 20, 25, 27, 29, 33, 34, 37, 42, 51, 55, 56, 57, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 19, 30, 34, 37, 38, 41, 43, 46, 52, 53, 54, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 19, 20, 21, 33, 35, 37, 38, 43, 49, 51, 55, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 19, 20, 21, 33, 34, 35, 37, 38, 45, 49, 51, 53, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 19, 26, 30, 41, 43, 44, 47, 52, 53, 54, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 21, 34, 36, 37, 49, 51, 53, 54, 56, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 21, 25, 34, 37, 39, 48, 51, 53, 54, 57, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 21, 23, 36, 37, 44, 49, 51, 54, 55, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 20, 21, 34, 37, 38, 49, 51, 53, 54, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 20, 21, 23, 37, 38, 44, 49, 51, 54, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 21, 36, 42, 43, 49, 51, 54, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 21, 34, 36, 42, 49, 51, 53, 54, 56, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 21, 34, 36, 42, 45, 49, 51, 53, 54, 56, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 21, 25, 39, 42, 43, 48, 51, 54, 55, 57, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 21, 25, 34, 39, 42, 48, 51, 53, 54, 57, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 21, 23, 36, 42, 44, 49, 51, 54, 55, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 19, 21, 38, 42, 43, 49, 51, 54, 55, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 19, 21, 34, 38, 42, 49, 51, 53, 54, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 19, 21, 34, 38, 42, 45, 49, 51, 53, 54, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 19, 21, 23, 38, 42, 44, 49, 51, 54, 55, 61, 62, 63 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 707 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS114[1], DS114[2], DS114[3], DS114[17], DS114[33], DS114[34], DS114[45], DS114[46], DS114[47], DS114[48], DS114[56], DS114[57], DS114[59], DS114[60], DS114[61], DS114[67], DS114[71], DS114[77], DS114[78], DS114[82], DS114[91], DS114[100], DS114[103], DS114[107], DS114[122], DS114[124], DS114[131], DS114[132], DS114[133], DS114[134], DS114[135], DS114[150], DS114[151], DS114[152], DS114[153], DS114[154], DS114[157], DS114[160], DS114[162], DS114[170], DS114[173], DS114[174], DS114[175], DS114[176], DS114[177], DS114[186], DS114[200], DS114[209], DS114[212], DS114[215], DS114[216], DS114[232], DS114[234], DS114[235], DS114[244], DS114[247], DS114[248], DS114[249], DS114[250], DS114[251], DS114[252], DS114[258], DS114[267], DS114[274], DS114[277], DS114[280], DS114[283], DS114[287], DS114[291], DS114[297], DS114[306], DS114[307], DS114[308], DS114[316], DS114[317], DS114[319], DS114[320], DS114[322], DS114[323], DS114[325], DS114[327], DS114[328], DS114[331], DS114[335], DS114[336], DS114[337], DS114[338], DS114[342], DS114[343], DS114[344], DS114[345], DS114[346], DS114[347], DS114[353], DS114[358], DS114[368], DS114[371], DS114[378], DS114[381], DS114[385], DS114[388], DS114[389], DS114[403], DS114[407], DS114[410], DS114[413], DS114[418], DS114[422], DS114[426], DS114[428], DS114[429], DS114[431], DS114[433], DS114[434], DS114[435], DS114[436], DS114[437], DS114[438], DS114[451], DS114[453], DS114[454], DS114[455], DS114[477], DS114[478], DS114[479], DS114[480], DS114[485], DS114[491], DS114[497], DS114[498], DS114[499], DS114[500], DS114[501], DS114[502], DS114[503], DS114[504], DS114[505], DS114[506], DS114[507], DS114[508], DS114[509], DS114[510], DS114[511], DS114[512], DS114[513], DS114[514], DS114[515], DS114[516], DS114[517], DS114[518], DS114[519], DS114[520], DS114[521], DS114[522], DS114[523], DS114[524], DS114[525], DS114[526], DS114[527], DS114[528], DS114[531], DS114[532], DS114[533], DS114[534], DS114[543], DS114[545], DS114[547], DS114[548], DS114[549], DS114[550], DS114[551], DS114[552], DS114[553], DS114[554], DS114[556], DS114[557], DS114[559], DS114[561], DS114[562], DS114[574], DS114[580], DS114[581], DS114[582], DS114[583], DS114[584], DS114[585], DS114[586], DS114[587], DS114[588], DS114[589], DS114[590], DS114[593], DS114[594], DS114[597], DS114[598], DS114[599], DS114[600], DS114[601], DS114[602], DS114[603], DS114[604], DS114[605], DS114[606], DS114[607], DS114[608], DS114[609], DS114[610], DS114[611], DS114[612], DS114[613], DS114[614], DS114[615], DS114[616], DS114[617], DS114[618], DS114[619], DS114[620], DS114[621], DS114[622], DS114[623], DS114[624], DS114[625], DS114[626], DS114[627], DS114[628], DS114[629], DS114[630], DS114[631], DS114[632], DS114[633], DS114[634], DS114[635], DS114[636], DS114[637], DS114[638], DS114[639], DS114[641], DS114[643], DS114[652], DS114[664], DS114[665], DS114[667], DS114[669], DS114[670], DS114[671], DS114[672], DS114[673], DS114[674], DS114[675], DS114[676], DS114[677], DS114[678], DS114[679], DS114[680], DS114[681], DS114[682], DS114[683], DS114[684], DS114[685], DS114[686], DS114[687], DS114[688], DS114[689], DS114[690], DS114[691], DS114[692], DS114[693], DS114[694], DS114[695], DS114[696], DS114[697], DS114[699], DS114[700], DS114[701], DS114[704], DS114[705], DS114[706], DS114[707], DS114[708], DS114[710], DS114[711], DS114[713], DS114[714], DS114[715], DS114[716], DS114[717], DS114[718], DS114[719], DS114[720], DS114[721], DS114[722], DS114[723], DS114[724], DS114[725], DS114[726], DS114[727], DS114[728], DS114[729], DS114[731], DS114[734], DS114[740], DS114[741], DS114[742], DS114[743], DS114[744], DS114[745], DS114[746], DS114[747], DS114[748], DS114[749], DS114[750], DS114[751], DS114[752], DS114[753], DS114[754], DS114[757], DS114[758], DS114[759], DS114[760], DS114[761], DS114[783], DS114[784], DS114[786], DS114[787], DS114[788], DS114[789], DS114[790], DS114[791], DS114[792], DS114[793], DS114[794], DS114[795], DS114[796], DS114[797], DS114[798], DS114[799], DS114[800], DS114[801], DS114[802], DS114[803], DS114[804], DS114[805], DS114[806], DS114[807], DS114[809], DS114[810], DS114[811], DS114[812], DS114[813], DS114[814], DS114[815], DS114[816], DS114[817], DS114[818], DS114[821], DS114[825], DS114[828], DS114[832], DS114[836], DS114[844], DS114[846], DS114[858], DS114[859], DS114[860], DS114[861], DS114[862], DS114[863], DS114[864], DS114[865], DS114[866], DS114[867], DS114[868], DS114[869], DS114[870], DS114[871], DS114[872], DS114[874], DS114[876], DS114[877], DS114[878], DS114[879], DS114[880], DS114[881], DS114[882], DS114[883], DS114[884], DS114[885], DS114[886], DS114[887], DS114[888], DS114[889], DS114[890], DS114[891], DS114[892], DS114[893], DS114[894], DS114[895], DS114[896], DS114[897], DS114[898], DS114[899], DS114[900], DS114[901], DS114[902], DS114[903], DS114[904], DS114[905], DS114[906], DS114[908], DS114[909], DS114[910], DS114[911], DS114[912], DS114[913], DS114[914], DS114[915], DS114[916], DS114[919], DS114[925], DS114[926], DS114[927], DS114[928], DS114[931], DS114[932], DS114[933], DS114[934], DS114[935], DS114[936], DS114[939], DS114[940], DS114[941], DS114[942], DS114[943], DS114[944], DS114[945], DS114[946], DS114[947], DS114[948], DS114[949], DS114[950], DS114[955], DS114[956], DS114[957], DS114[958], DS114[959], DS114[960], DS114[961], DS114[962], DS114[963], DS114[964], DS114[965], DS114[966], DS114[967], DS114[968], DS114[969], DS114[970], DS114[971], DS114[972], DS114[973], DS114[974], DS114[975], DS114[976], DS114[977], DS114[978], DS114[979], DS114[980], DS114[981], DS114[982], DS114[983], DS114[984], DS114[985], DS114[986], DS114[987], DS114[988], DS114[989], DS114[990], DS114[991], DS114[993], DS114[996], DS114[997], DS114[998], DS114[999], DS114[1000], DS114[1001], DS114[1002], DS114[1003], DS114[1004], DS114[1005], DS114[1008], DS114[1010], DS114[1011], DS114[1012], DS114[1013], DS114[1014], DS114[1015], DS114[1016], DS114[1017], DS114[1018], DS114[1019], DS114[1020], DS114[1021], DS114[1022], DS114[1023], DS114[1024], DS114[1025], DS114[1026], DS114[1027], DS114[1028], DS114[1029], DS114[1030], DS114[1031], DS114[1032], DS114[1033], DS114[1034], DS114[1035], DS114[1036], DS114[1037], DS114[1038], DS114[1039], DS114[1040], DS114[1041], DS114[1042], DS114[1043], DS114[1044], DS114[1045], DS114[1046], DS114[1047], DS114[1048], DS114[1049], DS114[1050], DS114[1051], DS114[1052], DS114[1053], DS114[1054], DS114[1055], DS114[1056], DS114[1057], DS114[1058], DS114[1059], DS114[1060], DS114[1061], DS114[1062], DS114[1063], DS114[1064], DS114[1065], DS114[1066], DS114[1067], DS114[1068], DS114[1069], DS114[1070], DS114[1071], DS114[1072], DS114[1073], DS114[1074], DS114[1075], DS114[1076], DS114[1077], DS114[1078], DS114[1079], DS114[1080], DS114[1081], DS114[1082], DS114[1083], DS114[1084], DS114[1085], DS114[1086], DS114[1087], DS114[1088], DS114[1089], DS114[1090], DS114[1091], DS114[1092], DS114[1093], DS114[1094], DS114[1097], DS114[1098], DS114[1099], DS114[1100], DS114[1101], DS114[1102], DS114[1103], DS114[1104], DS114[1105], DS114[1106], DS114[1107], DS114[1108], DS114[1109], DS114[1110], DS114[1111], DS114[1112], DS114[1113], DS114[1114], DS114[1115], DS114[1116], DS114[1119], DS114[1120], DS114[1121], DS114[1122], DS114[1123], DS114[1124], DS114[1125], DS114[1126], DS114[1127], DS114[1128], DS114[1129], DS114[1133], DS114[1138], DS114[1139], DS114[1142], DS114[1143], DS114[1144], DS114[1145], DS114[1146], DS114[1147], DS114[1148], DS114[1149], DS114[1150], DS114[1151], DS114[1153], DS114[1154], DS114[1155], DS114[1156], DS114[1157], DS114[1158], DS114[1159], DS114[1160], DS114[1161], DS114[1162], DS114[1163], DS114[1164], DS114[1165], DS114[1166], DS114[1167], DS114[1168], DS114[1169], DS114[1170], DS114[1171], DS114[1172], DS114[1173], DS114[1174], DS114[1175], DS114[1176], DS114[1177], DS114[1178], DS114[1179], DS114[1181], DS114[1182], DS114[1183], DS114[1184], DS114[1186], DS114[1187], DS114[1188], DS114[1189], DS114[1190], DS114[1191], DS114[1192], DS114[1193], DS114[1194], DS114[1195], DS114[1197], DS114[1198], DS114[1199], DS114[1200], DS114[1201], DS114[1202], DS114[1203], DS114[1204], DS114[1205], DS114[1206], DS114[1207], DS114[1208], DS114[1209], DS114[1210], DS114[1211], DS114[1212], DS114[1213], DS114[1214], DS114[1215], DS114[1216], DS114[1217], DS114[1218], DS114[1219], DS114[1220], DS114[1221], DS114[1222], DS114[1223], DS114[1224], DS114[1225], DS114[1226], DS114[1227], DS114[1228], DS114[1229], DS114[1230], DS114[1231], DS114[1232], DS114[1233], DS114[1234], DS114[1235], DS114[1236], DS114[1237], DS114[1238], DS114[1239], DS114[1240], DS114[1241], DS114[1242], DS114[1243], DS114[1244]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,114]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,114] is 52 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,114] is RDS114:=[ [ 2, 4, 8, 9, 11, 12, 13, 15, 17, 23, 24, 29, 32, 36, 38, 39, 41, 44, 48, 49, 54, 55, 56, 59, 61, 62, 63, 64 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 17, 23, 24, 29, 32, 34, 36, 38, 39, 41, 44, 48, 49, 53, 54, 56, 59, 61, 62, 64 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 17, 18, 23, 24, 29, 32, 34, 36, 38, 44, 48, 49, 53, 54, 56, 57, 59, 61, 62, 64 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 17, 20, 22, 23, 24, 29, 32, 39, 41, 42, 44, 48, 49, 54, 55, 59, 61, 62, 63, 64 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 17, 20, 22, 23, 24, 29, 32, 34, 39, 41, 42, 44, 48, 49, 53, 54, 59, 61, 62, 64 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 17, 18, 20, 22, 23, 24, 29, 32, 34, 42, 44, 48, 49, 53, 54, 57, 59, 61, 62, 64 ], [ 2, 4, 5, 6, 8, 11, 12, 13, 15, 17, 18, 21, 22, 23, 24, 32, 36, 38, 44, 48, 54, 55, 56, 57, 59, 61, 63, 64 ], [ 2, 4, 5, 6, 8, 11, 12, 13, 15, 17, 18, 21, 22, 23, 24, 32, 34, 36, 38, 44, 48, 53, 54, 56, 57, 59, 61, 64 ], [ 2, 3, 5, 6, 8, 9, 15, 16, 21, 22, 25, 27, 30, 31, 32, 34, 38, 45, 47, 51, 53, 55, 59, 60, 61, 62, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 15, 16, 21, 22, 23, 25, 27, 30, 31, 32, 34, 38, 43, 44, 47, 51, 53, 55, 58, 61, 62, 63 ], [ 2, 3, 5, 6, 8, 9, 15, 16, 21, 22, 23, 24, 27, 30, 31, 32, 34, 38, 44, 48, 51, 53, 55, 59, 61, 62, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 13, 15, 16, 21, 22, 25, 27, 30, 31, 32, 33, 35, 38, 45, 47, 51, 54, 59, 60, 61, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 13, 15, 16, 21, 22, 23, 25, 27, 30, 31, 32, 33, 35, 38, 43, 44, 47, 51, 54, 58, 61, 62 ], [ 2, 3, 5, 6, 8, 9, 13, 15, 16, 21, 22, 23, 24, 27, 30, 31, 32, 33, 35, 38, 44, 48, 51, 54, 59, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 17, 23, 24, 29, 32, 37, 39, 41, 44, 48, 49, 54, 55, 59, 61, 62, 63, 64 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 17, 23, 24, 29, 32, 34, 37, 39, 41, 44, 48, 49, 53, 54, 59, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 17, 18, 23, 24, 29, 32, 34, 37, 44, 48, 49, 53, 54, 57, 59, 61, 62, 64 ], [ 2, 3, 4, 6, 8, 11, 12, 13, 16, 17, 18, 20, 22, 24, 32, 36, 42, 43, 45, 48, 54, 55, 56, 57, 58, 60, 61, 63 ], [ 2, 3, 4, 6, 8, 11, 12, 13, 16, 17, 18, 20, 22, 24, 32, 34, 36, 42, 43, 45, 48, 53, 54, 56, 57, 58, 60, 61 ], [ 2, 3, 4, 6, 8, 11, 12, 13, 16, 17, 18, 20, 22, 23, 24, 32, 36, 42, 44, 48, 54, 55, 56, 57, 59, 61, 63, 64 ], [ 2, 3, 4, 6, 8, 11, 12, 13, 16, 17, 18, 20, 22, 23, 24, 32, 34, 36, 42, 44, 48, 53, 54, 56, 57, 59, 61, 64 ], [ 2, 3, 4, 5, 8, 9, 16, 17, 19, 20, 21, 25, 27, 30, 31, 32, 36, 40, 42, 45, 47, 51, 56, 59, 60, 61, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 16, 17, 19, 20, 21, 23, 25, 27, 30, 31, 32, 36, 40, 42, 43, 44, 47, 51, 56, 58, 61, 62 ], [ 2, 3, 4, 5, 8, 9, 16, 17, 19, 20, 21, 23, 24, 27, 30, 31, 32, 36, 40, 42, 44, 48, 51, 56, 59, 61, 62, 64 ], [ 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 17, 18, 21, 22, 23, 24, 32, 37, 44, 48, 54, 55, 57, 59, 61, 63, 64 ], [ 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 17, 18, 21, 22, 23, 24, 32, 34, 37, 44, 48, 53, 54, 57, 59, 61, 64 ], [ 2, 3, 4, 5, 6, 8, 9, 15, 16, 17, 19, 21, 22, 25, 27, 30, 31, 32, 38, 40, 45, 47, 51, 59, 60, 61, 62, 64 ], [ 2, 3, 4, 5, 6, 8, 9, 15, 16, 17, 19, 21, 22, 23, 25, 27, 30, 31, 32, 38, 40, 43, 44, 47, 51, 58, 61, 62 ], [ 2, 3, 4, 5, 6, 8, 9, 15, 16, 17, 19, 21, 22, 23, 24, 27, 30, 31, 32, 38, 40, 44, 48, 51, 59, 61, 62, 64 ], [ 1, 2, 4, 7, 8, 11, 12, 13, 15, 17, 18, 20, 23, 24, 32, 36, 38, 42, 44, 48, 54, 55, 56, 57, 59, 61, 63, 64 ], [ 1, 2, 4, 7, 8, 11, 12, 13, 15, 17, 18, 20, 23, 24, 32, 34, 36, 38, 42, 44, 48, 53, 54, 56, 57, 59, 61, 64 ], [ 1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 17, 21, 23, 24, 29, 32, 39, 41, 44, 48, 49, 54, 55, 59, 61, 62, 63, 64 ], [ 1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 17, 21, 23, 24, 29, 32, 34, 39, 41, 44, 48, 49, 53, 54, 59, 61, 62, 64 ], [ 1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 17, 18, 21, 23, 24, 29, 32, 34, 44, 48, 49, 53, 54, 57, 59, 61, 62, 64 ], [ 1, 2, 3, 6, 7, 8, 9, 16, 22, 25, 27, 30, 31, 32, 34, 36, 45, 47, 51, 53, 55, 56, 59, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 6, 7, 8, 9, 16, 22, 23, 25, 27, 30, 31, 32, 34, 36, 43, 44, 47, 51, 53, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 6, 7, 8, 9, 16, 22, 23, 24, 27, 30, 31, 32, 34, 36, 44, 48, 51, 53, 55, 56, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 6, 7, 8, 9, 13, 16, 22, 25, 27, 30, 31, 32, 33, 35, 36, 45, 47, 51, 54, 56, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 6, 7, 8, 9, 13, 16, 22, 23, 25, 27, 30, 31, 32, 33, 35, 36, 43, 44, 47, 51, 54, 56, 58, 61, 62 ], [ 1, 2, 3, 6, 7, 8, 9, 13, 16, 22, 23, 24, 27, 30, 31, 32, 33, 35, 36, 44, 48, 51, 54, 56, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 7, 8, 11, 12, 13, 14, 16, 17, 18, 20, 23, 24, 32, 37, 42, 44, 48, 54, 55, 57, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 7, 8, 11, 12, 13, 14, 16, 17, 18, 20, 23, 24, 32, 34, 37, 42, 44, 48, 53, 54, 57, 59, 61, 64 ], [ 1, 2, 3, 4, 7, 8, 9, 15, 16, 17, 19, 20, 25, 27, 30, 31, 32, 38, 40, 42, 45, 47, 51, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 7, 8, 9, 15, 16, 17, 19, 20, 23, 25, 27, 30, 31, 32, 38, 40, 42, 43, 44, 47, 51, 58, 61, 62 ], [ 1, 2, 3, 4, 7, 8, 9, 15, 16, 17, 19, 20, 23, 24, 27, 30, 31, 32, 38, 40, 42, 44, 48, 51, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 16, 17, 19, 22, 25, 27, 30, 31, 32, 36, 40, 45, 47, 51, 56, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 16, 17, 19, 22, 23, 25, 27, 30, 31, 32, 36, 40, 43, 44, 47, 51, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 16, 17, 19, 22, 23, 24, 27, 30, 31, 32, 36, 40, 44, 48, 51, 56, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 12, 13, 16, 17, 18, 21, 24, 32, 36, 43, 45, 48, 54, 55, 56, 57, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 12, 13, 16, 17, 18, 21, 24, 32, 34, 36, 43, 45, 48, 53, 54, 56, 57, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 12, 13, 16, 17, 18, 21, 23, 24, 32, 36, 44, 48, 54, 55, 56, 57, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 12, 13, 16, 17, 18, 21, 23, 24, 32, 34, 36, 44, 48, 53, 54, 56, 57, 59, 61, 64 ] ]; ########################### ########################### ###########################