### 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 [64,159]. 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 [64,159]. # 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(64,159));' can be # used to create a list e of the elements of the group [64,159]. # In our list of (64,28,12) DSs in group [64,159], we have [1, # 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, # 30, 35, 37, 40, 43, 49, 50, 51, 53, 57, 60, 63, 64]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[6], e[7], e[9], e[10], e[11], e[13], e[14], e[16], e[18], e[22], e[23], e[30], # e[35], e[37], e[40], e[43], e[49], e[50], e[51], e[53], e[57], e[60], e[63], e[64]] # where e is the list of the elements of the group [64,159] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,159));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 159] ### The number of inequivalent (64,28,12) DSs in group [64,159] is 1200 ### The list of all inequivalent (64,28,12) DSs in group [64,159] is DS159:=[ [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, 30, 35, 37, 40, 43, 49, 50, 51, 53, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, 30, 35, 37, 40, 43, 44, 49, 50, 51, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, 29, 30, 37, 40, 43, 49, 53, 54, 55, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, 29, 30, 37, 40, 43, 44, 49, 53, 54, 55, 57, 58, 62 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, 28, 30, 35, 37, 40, 43, 50, 53, 57, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, 28, 30, 35, 37, 40, 43, 44, 50, 53, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 18, 22, 30, 35, 36, 40, 44, 49, 50, 51, 53, 57, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 18, 22, 29, 30, 36, 40, 44, 49, 53, 54, 55, 57, 58, 60, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 18, 22, 28, 30, 35, 36, 40, 44, 50, 53, 57, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 18, 22, 23, 30, 35, 36, 40, 43, 45, 49, 50, 51, 53, 57, 59, 63 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 18, 22, 23, 29, 30, 36, 40, 43, 45, 49, 53, 54, 55, 57, 59, 62 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 18, 22, 23, 28, 30, 35, 36, 40, 43, 45, 50, 53, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 13, 15, 17, 19, 22, 23, 32, 35, 37, 40, 43, 44, 46, 47, 48, 52, 53, 56, 58, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 13, 15, 17, 19, 22, 23, 25, 32, 35, 37, 40, 43, 44, 47, 52, 53, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 15, 17, 22, 23, 25, 31, 35, 37, 41, 43, 47, 53, 56, 57, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 15, 17, 22, 23, 25, 31, 35, 37, 41, 43, 44, 47, 53, 56, 57, 58, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 15, 17, 18, 22, 23, 25, 31, 35, 37, 39, 43, 47, 53, 56, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 15, 17, 18, 22, 23, 25, 31, 35, 37, 39, 43, 44, 47, 53, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 11, 13, 15, 17, 19, 22, 23, 30, 35, 37, 40, 43, 44, 46, 47, 48, 53, 56, 58, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 11, 13, 15, 17, 19, 22, 23, 25, 30, 35, 37, 40, 43, 44, 47, 53, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 14, 16, 17, 18, 22, 23, 29, 31, 37, 39, 43, 46, 47, 48, 49, 52, 60, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 14, 16, 17, 18, 22, 23, 29, 31, 37, 39, 43, 44, 46, 47, 48, 49, 52, 58, 62 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 14, 15, 17, 18, 22, 29, 31, 36, 39, 44, 46, 47, 48, 49, 52, 58, 60, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 14, 15, 17, 18, 22, 23, 29, 31, 36, 39, 43, 45, 46, 47, 48, 49, 52, 59, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 30, 34, 35, 36, 40, 43, 49, 50, 51, 55, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 30, 34, 35, 36, 40, 43, 44, 49, 50, 51, 55, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 28, 30, 34, 35, 36, 40, 43, 50, 55, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 28, 30, 34, 35, 36, 40, 43, 44, 50, 55, 56, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 28, 29, 30, 36, 40, 43, 51, 53, 54, 55, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 28, 29, 30, 36, 40, 43, 44, 51, 53, 54, 55, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 30, 35, 38, 40, 43, 49, 50, 51, 53, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 30, 35, 38, 40, 43, 44, 49, 50, 51, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 29, 30, 38, 40, 43, 49, 53, 54, 55, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 29, 30, 38, 40, 43, 44, 49, 53, 54, 55, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 28, 30, 35, 38, 40, 43, 50, 53, 57, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 28, 30, 35, 38, 40, 43, 44, 50, 53, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 21, 23, 30, 35, 36, 39, 40, 41, 44, 45, 49, 50, 51, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 21, 23, 30, 34, 35, 36, 39, 40, 41, 45, 49, 50, 51, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 21, 23, 29, 30, 34, 36, 39, 40, 41, 44, 45, 49, 54, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 21, 23, 28, 30, 35, 36, 39, 40, 41, 44, 45, 50, 53, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 21, 23, 28, 30, 34, 35, 36, 39, 40, 41, 45, 50, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 21, 23, 28, 29, 30, 34, 36, 39, 40, 41, 45, 51, 54, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 19, 21, 23, 30, 34, 35, 36, 39, 44, 49, 50, 51, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 19, 21, 23, 28, 30, 34, 35, 36, 39, 50, 55, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 19, 21, 23, 28, 29, 30, 36, 39, 51, 53, 54, 55, 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53, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 30, 32, 33, 36, 38, 40, 49, 54, 56, 57, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 28, 30, 33, 36, 38, 40, 44, 48, 52, 54, 56, 57, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 22, 24, 26, 34, 36, 40, 42, 43, 49, 55, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 33, 38, 40, 41, 42, 46, 48, 49, 54, 55, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 24, 38, 40, 41, 42, 47, 48, 49, 53, 55, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 22, 23, 35, 39, 40, 44, 46, 48, 54, 55, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 23, 32, 37, 38, 39, 45, 48, 49, 51, 52, 53, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 23, 32, 36, 37, 39, 45, 46, 49, 51, 52, 55, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 23, 29, 32, 37, 38, 44, 48, 50, 52, 57, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 23, 32, 34, 36, 37, 39, 40, 46, 49, 52, 53, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 32, 33, 36, 37, 39, 46, 52, 54, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 32, 33, 34, 37, 38, 39, 44, 48, 52, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 32, 34, 37, 38, 40, 44, 48, 52, 53, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 23, 26, 36, 38, 39, 40, 41, 47, 48, 49, 53, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 20, 22, 23, 26, 39, 40, 47, 48, 53, 55, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 19, 23, 26, 36, 38, 39, 40, 47, 48, 57, 62, 63, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 726 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS159[2], DS159[3], DS159[5], DS159[6], DS159[8], DS159[10], DS159[11], DS159[13], DS159[15], DS159[16], DS159[17], DS159[19], DS159[20], DS159[21], DS159[22], DS159[25], DS159[26], DS159[27], DS159[28], DS159[29], DS159[31], DS159[32], DS159[34], DS159[35], DS159[36], DS159[38], DS159[39], DS159[42], DS159[45], DS159[51], DS159[52], DS159[54], DS159[59], DS159[61], DS159[62], DS159[65], DS159[68], DS159[70], DS159[71], DS159[72], DS159[76], DS159[77], DS159[80], DS159[81], DS159[82], DS159[83], DS159[84], DS159[88], DS159[93], DS159[95], DS159[96], DS159[97], DS159[99], DS159[102], DS159[108], DS159[109], DS159[111], DS159[112], DS159[117], DS159[118], DS159[129], DS159[132], DS159[133], DS159[135], DS159[136], DS159[140], DS159[147], DS159[148], DS159[151], DS159[152], DS159[153], DS159[154], DS159[158], DS159[159], DS159[160], DS159[161], DS159[162], DS159[165], DS159[166], DS159[168], DS159[170], DS159[171], DS159[174], DS159[175], DS159[190], DS159[192], DS159[195], DS159[196], DS159[199], DS159[201], DS159[207], DS159[208], DS159[209], DS159[210], DS159[211], DS159[212], DS159[213], DS159[214], DS159[215], DS159[217], DS159[218], DS159[219], DS159[221], DS159[233], DS159[234], DS159[235], DS159[236], DS159[237], DS159[241], DS159[242], DS159[243], DS159[244], DS159[245], DS159[246], DS159[252], DS159[257], DS159[258], DS159[262], DS159[264], DS159[266], DS159[270], DS159[271], DS159[272], DS159[273], DS159[274], DS159[275], DS159[276], DS159[277], DS159[278], DS159[287], DS159[293], DS159[294], DS159[295], DS159[297], DS159[300], DS159[308], DS159[309], DS159[310], DS159[312], DS159[315], DS159[316], DS159[317], DS159[321], DS159[322], DS159[323], DS159[324], DS159[325], DS159[326], DS159[327], DS159[328], DS159[330], DS159[336], DS159[339], DS159[345], DS159[346], DS159[347], DS159[354], DS159[356], DS159[361], DS159[363], DS159[379], DS159[380], DS159[382], DS159[383], DS159[384], DS159[385], DS159[386], DS159[388], DS159[389], DS159[392], DS159[394], DS159[395], DS159[397], DS159[398], DS159[399], DS159[400], DS159[403], DS159[404], DS159[406], DS159[407], DS159[408], DS159[409], DS159[411], DS159[413], DS159[414], DS159[416], DS159[417], DS159[419], DS159[421], DS159[422], DS159[425], DS159[426], DS159[427], DS159[428], DS159[436], DS159[437], DS159[438], DS159[439], DS159[440], DS159[441], DS159[442], DS159[445], DS159[446], DS159[448], DS159[451], DS159[452], DS159[455], DS159[456], DS159[457], DS159[458], DS159[461], DS159[462], DS159[466], DS159[467], DS159[472], DS159[473], DS159[475], DS159[476], DS159[480], DS159[483], DS159[485], DS159[486], DS159[487], DS159[488], DS159[489], DS159[490], DS159[491], DS159[492], DS159[494], DS159[496], DS159[522], DS159[523], DS159[526], DS159[527], DS159[529], DS159[530], DS159[531], DS159[532], DS159[533], DS159[534], DS159[535], DS159[536], DS159[537], DS159[538], DS159[539], DS159[541], DS159[543], DS159[544], DS159[545], DS159[546], DS159[547], DS159[549], DS159[555], DS159[556], DS159[558], DS159[561], DS159[564], DS159[566], DS159[567], DS159[568], DS159[569], DS159[570], DS159[571], DS159[572], DS159[576], DS159[578], DS159[579], DS159[580], DS159[581], DS159[582], DS159[584], DS159[585], DS159[589], DS159[590], DS159[591], DS159[592], DS159[593], DS159[594], DS159[595], DS159[597], DS159[600], DS159[602], DS159[603], DS159[607], DS159[608], DS159[609], DS159[610], DS159[611], DS159[612], DS159[613], DS159[615], DS159[616], DS159[617], DS159[618], DS159[619], DS159[620], DS159[621], DS159[622], DS159[623], DS159[625], DS159[626], DS159[627], DS159[631], DS159[632], DS159[633], DS159[635], DS159[636], DS159[637], DS159[638], DS159[639], DS159[640], DS159[641], DS159[642], DS159[643], DS159[645], DS159[646], DS159[647], DS159[649], DS159[652], DS159[653], DS159[654], DS159[658], DS159[659], DS159[660], DS159[662], DS159[663], DS159[664], DS159[666], DS159[668], DS159[670], DS159[678], DS159[679], DS159[682], DS159[685], DS159[686], DS159[689], DS159[690], DS159[691], DS159[692], DS159[694], DS159[695], DS159[696], DS159[702], DS159[703], DS159[706], DS159[707], DS159[710], DS159[711], DS159[715], DS159[716], DS159[722], DS159[723], DS159[724], DS159[726], DS159[730], DS159[731], DS159[732], DS159[734], DS159[735], DS159[737], DS159[738], DS159[741], DS159[744], DS159[746], DS159[752], DS159[765], DS159[778], DS159[782], DS159[783], DS159[785], DS159[787], DS159[790], DS159[792], DS159[794], DS159[795], DS159[805], DS159[806], DS159[808], DS159[815], DS159[816], DS159[817], DS159[818], DS159[819], DS159[820], DS159[823], DS159[827], DS159[829], DS159[830], DS159[831], DS159[832], DS159[833], DS159[834], DS159[836], DS159[837], DS159[841], DS159[842], DS159[843], DS159[844], DS159[845], DS159[846], DS159[847], DS159[848], DS159[849], DS159[850], DS159[851], DS159[852], DS159[853], DS159[854], DS159[855], DS159[856], DS159[857], DS159[858], DS159[859], DS159[860], DS159[861], DS159[862], DS159[863], DS159[864], DS159[865], DS159[866], DS159[867], DS159[868], DS159[869], DS159[870], DS159[871], DS159[872], DS159[873], DS159[874], DS159[875], DS159[876], DS159[877], DS159[878], DS159[879], DS159[880], DS159[881], DS159[882], DS159[883], DS159[884], DS159[885], DS159[886], DS159[887], DS159[888], DS159[889], DS159[890], DS159[891], DS159[892], DS159[893], DS159[894], DS159[895], DS159[896], DS159[897], DS159[898], DS159[899], DS159[900], DS159[907], DS159[908], DS159[909], DS159[910], DS159[911], DS159[912], DS159[913], DS159[914], DS159[915], DS159[917], DS159[918], DS159[919], DS159[921], DS159[922], DS159[923], DS159[924], DS159[925], DS159[926], DS159[927], DS159[928], DS159[929], DS159[930], DS159[934], DS159[935], DS159[937], DS159[938], DS159[939], DS159[940], DS159[941], DS159[942], DS159[943], DS159[944], DS159[945], DS159[946], DS159[947], DS159[948], DS159[949], DS159[950], DS159[951], DS159[952], DS159[953], DS159[954], DS159[955], DS159[956], DS159[957], DS159[959], DS159[960], DS159[961], DS159[962], DS159[963], DS159[964], DS159[965], DS159[966], DS159[967], DS159[968], DS159[969], DS159[970], DS159[971], DS159[972], DS159[973], DS159[974], DS159[975], DS159[977], DS159[978], DS159[979], DS159[980], DS159[981], DS159[982], DS159[983], DS159[984], DS159[985], DS159[986], DS159[987], DS159[988], DS159[990], DS159[991], DS159[992], DS159[995], DS159[997], DS159[999], DS159[1000], DS159[1001], DS159[1002], DS159[1003], DS159[1004], DS159[1005], DS159[1006], DS159[1007], DS159[1008], DS159[1009], DS159[1010], DS159[1011], DS159[1012], DS159[1013], DS159[1014], DS159[1015], DS159[1016], DS159[1017], DS159[1018], DS159[1019], DS159[1020], DS159[1021], DS159[1022], DS159[1023], DS159[1024], DS159[1025], DS159[1026], DS159[1027], DS159[1028], DS159[1029], DS159[1030], DS159[1031], DS159[1032], DS159[1033], DS159[1034], DS159[1035], DS159[1036], DS159[1037], DS159[1038], DS159[1039], DS159[1040], DS159[1041], DS159[1042], DS159[1043], DS159[1044], DS159[1045], DS159[1046], DS159[1047], DS159[1048], DS159[1049], DS159[1050], DS159[1051], DS159[1052], DS159[1053], DS159[1054], DS159[1055], DS159[1056], DS159[1057], DS159[1058], DS159[1059], DS159[1060], DS159[1061], DS159[1062], DS159[1063], DS159[1064], DS159[1065], DS159[1066], DS159[1067], DS159[1068], DS159[1069], DS159[1070], DS159[1071], DS159[1072], DS159[1073], DS159[1074], DS159[1075], DS159[1076], DS159[1077], DS159[1078], DS159[1079], DS159[1080], DS159[1081], DS159[1082], DS159[1083], DS159[1084], DS159[1085], DS159[1086], DS159[1087], DS159[1088], DS159[1089], DS159[1090], DS159[1091], DS159[1092], DS159[1093], DS159[1094], DS159[1095], DS159[1097], DS159[1098], DS159[1099], DS159[1100], DS159[1104], DS159[1110], DS159[1111], DS159[1112], DS159[1113], DS159[1114], DS159[1115], DS159[1116], DS159[1117], DS159[1118], DS159[1119], DS159[1120], DS159[1121], DS159[1122], DS159[1123], DS159[1124], DS159[1125], DS159[1126], DS159[1127], DS159[1128], DS159[1129], DS159[1130], DS159[1131], DS159[1132], DS159[1133], DS159[1134], DS159[1135], DS159[1136], DS159[1137], DS159[1138], DS159[1139], DS159[1140], DS159[1141], DS159[1142], DS159[1143], DS159[1144], DS159[1145], DS159[1146], DS159[1147], DS159[1148], DS159[1149], DS159[1150], DS159[1151], DS159[1152], DS159[1153], DS159[1154], DS159[1155], DS159[1156], DS159[1157], DS159[1158], DS159[1159], DS159[1160], DS159[1161], DS159[1162], DS159[1163], DS159[1164], DS159[1165], DS159[1166], DS159[1167], DS159[1168], DS159[1169], DS159[1170], DS159[1171], DS159[1172], DS159[1173], DS159[1174], DS159[1175], DS159[1176], DS159[1177], DS159[1178], DS159[1179], DS159[1180], DS159[1181], DS159[1182], DS159[1183], DS159[1184], DS159[1185], DS159[1186], DS159[1187], DS159[1188], DS159[1189], DS159[1190], DS159[1191], DS159[1192], DS159[1193], DS159[1194], DS159[1195], DS159[1196], DS159[1197], DS159[1198], DS159[1199], DS159[1200]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,159]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,159] is 8 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,159] is RDS159:=[ [ 2, 4, 5, 9, 10, 11, 13, 15, 18, 20, 21, 23, 29, 30, 36, 38, 40, 42, 43, 49, 53, 54, 55, 56, 57, 60, 62, 64 ], [ 2, 4, 5, 8, 9, 10, 11, 13, 20, 21, 23, 24, 26, 29, 30, 34, 39, 40, 41, 42, 43, 47, 49, 54, 60, 62, 63, 64 ], [ 2, 4, 5, 8, 9, 10, 11, 13, 18, 20, 21, 23, 24, 26, 29, 30, 40, 42, 43, 47, 49, 53, 54, 55, 57, 60, 62, 64 ], [ 2, 3, 4, 5, 9, 10, 11, 13, 14, 16, 18, 20, 21, 23, 29, 30, 37, 40, 42, 43, 49, 53, 54, 55, 57, 60, 62, 64 ], [ 1, 2, 4, 6, 7, 9, 10, 11, 13, 15, 18, 22, 23, 29, 30, 36, 38, 40, 43, 49, 53, 54, 55, 56, 57, 60, 62, 64 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 22, 23, 24, 26, 29, 30, 34, 39, 40, 41, 43, 47, 49, 54, 60, 62, 63, 64 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 18, 22, 23, 24, 26, 29, 30, 40, 43, 47, 49, 53, 54, 55, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 18, 22, 23, 29, 30, 37, 40, 43, 49, 53, 54, 55, 57, 60, 62, 64 ] ]; ########################### 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