### 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 [64,137]. Also, we determine the nonisomorphic # symmetric (64,28,12) designs that rise from these DSs. # Note that there is no reversible (64,28,12) difference sets in # group [64,137]. # 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(64,137));' can be # used to create a list e of the elements of the group [64,137]. # In our list of (64,28,12) DSs in group [64,137], we have [1, # 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 19, 20, 27, 32, # 33, 35, 38, 39, 45, 51, 54, 56, 57, 59, 60, 62, 64]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[6], e[9], e[11], e[12], e[13], e[14], e[19], e[20], e[27], e[32], e[33], # e[35], e[38], e[39], e[45], e[51], e[54], e[56], e[57], e[59], e[60], e[62], e[64]] # where e is the list of the elements of the group [64,137] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,137));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 137] ### The number of inequivalent (64,28,12) DSs in group [64,137] is 1608 ### The list of all inequivalent (64,28,12) DSs in group [64,137] is DS137:=[ [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 19, 20, 27, 32, 33, 35, 38, 39, 45, 51, 54, 56, 57, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 19, 20, 23, 32, 33, 35, 38, 39, 44, 49, 50, 51, 54, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 19, 20, 27, 32, 33, 35, 36, 39, 43, 44, 45, 51, 54, 57, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 19, 20, 23, 32, 33, 35, 36, 39, 43, 49, 50, 51, 54, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 18, 19, 20, 23, 25, 30, 31, 32, 35, 38, 41, 43, 45, 47, 53, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 17, 19, 20, 25, 27, 28, 30, 31, 32, 34, 35, 38, 40, 47, 50, 51, 55, 56, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 17, 18, 24, 26, 34, 35, 36, 38, 42, 43, 46, 47, 49, 54, 57, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 24, 26, 27, 30, 34, 35, 39, 41, 42, 47, 49, 50, 52, 54, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 24, 25, 26, 27, 34, 35, 39, 41, 42, 44, 47, 48, 50, 54, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 23, 26, 27, 34, 35, 39, 41, 42, 44, 45, 50, 54, 56, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 23, 25, 26, 27, 34, 35, 39, 41, 42, 45, 46, 48, 50, 54, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 23, 25, 26, 27, 35, 42, 45, 46, 48, 50, 53, 54, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 15, 17, 18, 23, 26, 34, 36, 37, 42, 43, 44, 45, 49, 53, 54, 57, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 24, 26, 36, 38, 39, 40, 42, 43, 46, 47, 49, 54, 55, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 24, 26, 27, 30, 36, 38, 39, 40, 42, 47, 49, 50, 52, 54, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 25, 26, 28, 30, 33, 34, 36, 38, 39, 41, 42, 48, 49, 51, 52, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 24, 26, 27, 30, 33, 34, 36, 38, 39, 41, 42, 47, 49, 50, 52, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 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30, 33, 38, 43, 46, 52, 53, 55, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 30, 34, 41, 44, 46, 52, 53, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 24, 28, 34, 36, 37, 39, 42, 45, 49, 51, 54, 55, 56, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 24, 28, 33, 34, 36, 39, 41, 42, 44, 45, 46, 47, 54, 57 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 25, 26, 30, 34, 37, 43, 49, 51, 52, 53, 54, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 25, 26, 27, 30, 34, 37, 50, 51, 52, 53, 54, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 24, 30, 37, 39, 41, 44, 45, 46, 49, 52, 54, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 24, 25, 30, 37, 39, 41, 45, 48, 49, 52, 54, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 20, 24, 28, 34, 36, 40, 41, 42, 44, 45, 46, 47, 53, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 20, 24, 28, 37, 38, 39, 42, 45, 49, 51, 53, 54, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 35, 38, 40, 52, 54, 55, 56, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 35, 38, 40, 43, 46, 52, 54, 55, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 35, 36, 38, 39, 40, 46, 49, 52, 54, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 34, 35, 38, 39, 40, 44, 49, 52, 54, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 34, 35, 36, 38, 40, 44, 46, 52, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 34, 35, 36, 38, 40, 43, 44, 46, 49, 52, 54, 57 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 33, 35, 36, 38, 40, 52, 55, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 33, 35, 36, 38, 40, 43, 46, 52, 55, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 33, 34, 35, 36, 38, 39, 40, 44, 46, 52, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 33, 34, 35, 36, 38, 39, 40, 43, 44, 46, 49, 52 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 30, 33, 36, 38, 52, 53, 54, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 30, 33, 36, 38, 46, 49, 52, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 20, 27, 34, 36, 42, 44, 47, 50, 54, 55, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 28, 30, 34, 36, 37, 41, 43, 44, 45, 46, 49, 52, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 27, 28, 30, 34, 36, 37, 41, 44, 45, 46, 50, 52, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 35, 37, 41, 52, 54, 55, 56, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 35, 37, 41, 43, 46, 52, 54, 55, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 35, 36, 37, 39, 41, 46, 49, 52, 54, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 34, 35, 37, 39, 41, 44, 49, 52, 54, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 34, 35, 36, 37, 41, 44, 46, 52, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 34, 35, 36, 37, 41, 43, 44, 46, 49, 52, 54, 57 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 33, 35, 36, 37, 41, 52, 55, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 33, 35, 36, 37, 41, 43, 46, 52, 55, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 33, 34, 35, 36, 37, 39, 41, 44, 46, 52, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 33, 34, 35, 36, 37, 39, 41, 43, 44, 46, 49, 52 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 30, 34, 36, 37, 52, 53, 55, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 30, 34, 36, 37, 46, 49, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 30, 33, 38, 39, 41, 43, 44, 46, 49, 52, 54, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 30, 34, 38, 39, 40, 43, 44, 46, 49, 52, 55, 63 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1037 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS137[2], DS137[4], DS137[14], DS137[30], DS137[33], DS137[60], DS137[85], DS137[88], DS137[89], DS137[103], DS137[126], DS137[132], DS137[133], DS137[134], DS137[141], DS137[148], DS137[150], DS137[151], DS137[152], DS137[153], DS137[154], DS137[168], DS137[169], DS137[174], DS137[179], DS137[188], DS137[192], DS137[213], DS137[214], DS137[215], DS137[216], DS137[217], DS137[228], DS137[230], DS137[239], DS137[240], DS137[241], DS137[255], DS137[269], DS137[273], DS137[280], DS137[287], DS137[299], DS137[302], DS137[305], DS137[306], DS137[308], DS137[310], DS137[315], DS137[316], DS137[322], DS137[327], DS137[329], DS137[331], DS137[332], DS137[336], DS137[346], DS137[347], DS137[351], DS137[355], DS137[365], DS137[368], DS137[379], DS137[380], DS137[381], DS137[383], DS137[384], DS137[388], DS137[391], DS137[392], DS137[394], DS137[397], DS137[401], DS137[402], DS137[403], DS137[406], DS137[409], DS137[412], DS137[416], DS137[418], DS137[421], DS137[422], DS137[425], DS137[426], DS137[427], DS137[428], DS137[429], DS137[430], DS137[431], DS137[433], DS137[435], DS137[436], DS137[437], DS137[438], DS137[441], DS137[442], DS137[446], DS137[455], DS137[456], DS137[459], DS137[460], DS137[461], DS137[463], DS137[470], DS137[473], DS137[474], DS137[476], DS137[477], DS137[478], DS137[480], DS137[483], DS137[484], DS137[485], DS137[488], DS137[489], DS137[490], DS137[497], DS137[499], DS137[500], DS137[501], DS137[503], DS137[508], DS137[509], DS137[513], DS137[514], DS137[522], DS137[524], DS137[525], DS137[529], DS137[530], DS137[535], DS137[538], DS137[542], DS137[544], DS137[547], DS137[550], DS137[552], DS137[555], DS137[556], DS137[557], DS137[558], DS137[559], DS137[560], DS137[571], DS137[573], DS137[574], DS137[575], DS137[576], DS137[577], DS137[580], DS137[583], DS137[587], DS137[593], DS137[594], DS137[597], DS137[602], DS137[605], DS137[609], DS137[612], DS137[614], DS137[616], DS137[617], DS137[618], DS137[619], DS137[620], DS137[627], DS137[631], DS137[634], DS137[638], DS137[639], DS137[640], DS137[641], DS137[642], DS137[644], DS137[645], DS137[646], DS137[647], DS137[648], DS137[649], DS137[650], DS137[651], DS137[652], DS137[654], DS137[655], DS137[656], DS137[661], DS137[665], DS137[667], DS137[671], DS137[673], DS137[674], DS137[675], DS137[676], DS137[679], DS137[681], DS137[683], DS137[684], DS137[685], DS137[688], DS137[689], DS137[691], DS137[692], DS137[693], DS137[694], DS137[698], DS137[701], DS137[705], DS137[706], DS137[708], DS137[710], DS137[711], DS137[714], DS137[715], DS137[716], DS137[717], DS137[718], DS137[719], DS137[720], DS137[721], DS137[722], DS137[723], DS137[724], DS137[725], DS137[726], DS137[727], DS137[728], DS137[729], DS137[730], DS137[731], DS137[732], DS137[733], DS137[734], DS137[735], DS137[736], DS137[737], DS137[738], DS137[739], DS137[740], DS137[741], DS137[742], DS137[743], DS137[744], DS137[745], DS137[746], DS137[748], DS137[749], DS137[750], DS137[751], DS137[752], DS137[753], DS137[754], DS137[755], DS137[756], DS137[757], DS137[758], DS137[759], DS137[760], DS137[761], DS137[762], DS137[763], DS137[764], DS137[765], DS137[766], DS137[767], DS137[768], DS137[769], DS137[770], DS137[771], DS137[772], DS137[773], DS137[774], DS137[775], DS137[776], DS137[777], DS137[778], DS137[779], DS137[780], DS137[781], DS137[782], DS137[783], DS137[784], DS137[785], DS137[786], DS137[787], DS137[788], DS137[789], DS137[790], DS137[791], DS137[792], DS137[793], DS137[794], DS137[795], DS137[796], DS137[797], DS137[798], DS137[799], DS137[800], DS137[801], DS137[802], DS137[803], DS137[804], DS137[805], DS137[806], DS137[808], DS137[809], DS137[810], DS137[811], DS137[812], DS137[813], DS137[814], DS137[815], DS137[816], DS137[817], DS137[818], DS137[819], DS137[820], DS137[821], DS137[822], DS137[823], DS137[824], DS137[825], DS137[826], DS137[830], DS137[831], DS137[832], DS137[833], DS137[834], DS137[835], DS137[836], DS137[837], DS137[838], DS137[839], DS137[840], DS137[841], DS137[842], DS137[843], DS137[844], DS137[845], DS137[846], DS137[847], DS137[848], DS137[849], DS137[850], DS137[851], DS137[852], DS137[853], DS137[854], DS137[855], DS137[856], DS137[857], DS137[858], DS137[859], DS137[860], DS137[861], DS137[862], DS137[863], DS137[864], DS137[865], DS137[866], DS137[867], DS137[868], DS137[869], DS137[870], DS137[871], DS137[872], DS137[873], DS137[874], DS137[875], DS137[876], DS137[877], DS137[878], DS137[879], DS137[880], DS137[881], DS137[882], DS137[885], DS137[886], DS137[887], DS137[888], DS137[889], DS137[890], DS137[891], DS137[892], DS137[893], DS137[894], DS137[895], DS137[896], DS137[897], DS137[898], DS137[899], DS137[900], DS137[901], DS137[902], DS137[903], DS137[905], DS137[906], DS137[909], DS137[910], DS137[911], DS137[920], DS137[921], DS137[922], DS137[923], DS137[924], DS137[925], DS137[926], DS137[927], DS137[928], DS137[929], DS137[930], DS137[931], DS137[932], DS137[933], DS137[934], DS137[935], DS137[936], DS137[937], DS137[938], DS137[939], DS137[940], DS137[941], DS137[942], DS137[943], DS137[944], DS137[945], DS137[946], DS137[947], DS137[948], DS137[949], DS137[950], DS137[951], DS137[952], DS137[953], DS137[954], DS137[955], DS137[956], DS137[957], DS137[958], DS137[959], DS137[960], DS137[961], DS137[962], DS137[963], DS137[964], DS137[965], DS137[966], DS137[967], DS137[968], DS137[969], DS137[970], DS137[971], DS137[972], DS137[973], DS137[974], DS137[975], DS137[976], DS137[977], DS137[978], DS137[979], DS137[980], DS137[981], DS137[982], DS137[983], DS137[984], DS137[985], DS137[986], DS137[987], DS137[988], DS137[989], DS137[990], DS137[991], DS137[992], DS137[993], DS137[994], DS137[995], DS137[996], DS137[997], DS137[998], DS137[999], DS137[1000], DS137[1001], DS137[1002], DS137[1003], DS137[1004], DS137[1005], DS137[1006], DS137[1007], DS137[1008], DS137[1009], DS137[1010], DS137[1011], DS137[1012], DS137[1013], DS137[1014], DS137[1015], DS137[1016], DS137[1017], DS137[1018], DS137[1019], DS137[1020], DS137[1021], DS137[1022], DS137[1023], DS137[1024], DS137[1025], DS137[1026], DS137[1027], DS137[1028], DS137[1029], DS137[1030], DS137[1031], DS137[1032], DS137[1034], DS137[1035], DS137[1036], DS137[1037], DS137[1038], DS137[1039], DS137[1040], DS137[1041], DS137[1042], DS137[1043], DS137[1044], DS137[1045], DS137[1046], DS137[1047], DS137[1048], DS137[1049], DS137[1050], DS137[1051], DS137[1052], DS137[1053], DS137[1054], DS137[1055], DS137[1056], DS137[1057], DS137[1058], DS137[1059], DS137[1076], DS137[1077], DS137[1078], DS137[1079], DS137[1080], DS137[1081], DS137[1082], DS137[1083], DS137[1084], DS137[1085], DS137[1088], DS137[1090], DS137[1091], DS137[1092], DS137[1094], DS137[1097], DS137[1098], DS137[1099], DS137[1100], DS137[1101], DS137[1102], DS137[1103], DS137[1104], DS137[1105], DS137[1106], DS137[1107], DS137[1108], DS137[1109], DS137[1110], DS137[1111], DS137[1112], DS137[1113], DS137[1114], DS137[1115], DS137[1116], DS137[1117], DS137[1118], DS137[1119], DS137[1120], DS137[1121], DS137[1122], DS137[1123], DS137[1124], DS137[1125], DS137[1126], DS137[1127], DS137[1128], DS137[1129], DS137[1130], DS137[1131], DS137[1132], DS137[1133], DS137[1134], DS137[1135], DS137[1136], DS137[1137], DS137[1138], DS137[1139], DS137[1140], DS137[1141], DS137[1142], DS137[1143], DS137[1144], DS137[1145], DS137[1146], DS137[1147], DS137[1148], DS137[1149], DS137[1150], DS137[1152], DS137[1153], DS137[1154], DS137[1155], DS137[1156], DS137[1157], DS137[1158], DS137[1159], DS137[1160], DS137[1161], DS137[1162], DS137[1163], DS137[1164], DS137[1166], DS137[1167], DS137[1168], DS137[1169], DS137[1170], DS137[1171], DS137[1174], DS137[1175], DS137[1176], DS137[1177], DS137[1178], DS137[1179], DS137[1181], DS137[1182], DS137[1183], DS137[1184], DS137[1185], DS137[1186], DS137[1189], DS137[1190], DS137[1191], DS137[1192], DS137[1193], DS137[1194], DS137[1195], DS137[1196], DS137[1197], DS137[1198], DS137[1199], DS137[1200], DS137[1201], DS137[1202], DS137[1203], DS137[1204], DS137[1205], DS137[1206], DS137[1207], DS137[1208], DS137[1209], DS137[1210], DS137[1211], DS137[1212], DS137[1213], DS137[1214], DS137[1215], DS137[1216], DS137[1217], DS137[1218], DS137[1219], DS137[1220], DS137[1221], DS137[1222], DS137[1223], DS137[1224], DS137[1225], DS137[1226], DS137[1227], DS137[1228], DS137[1229], DS137[1230], DS137[1231], DS137[1232], DS137[1233], DS137[1235], DS137[1236], DS137[1238], DS137[1239], DS137[1240], DS137[1241], DS137[1242], DS137[1243], DS137[1244], DS137[1245], DS137[1246], DS137[1247], DS137[1248], DS137[1249], DS137[1250], DS137[1251], DS137[1252], DS137[1253], DS137[1254], DS137[1255], DS137[1256], DS137[1257], DS137[1258], DS137[1259], DS137[1260], DS137[1261], DS137[1262], DS137[1263], DS137[1264], DS137[1265], DS137[1266], DS137[1267], DS137[1268], DS137[1269], DS137[1271], DS137[1272], DS137[1273], DS137[1274], DS137[1275], DS137[1276], DS137[1277], DS137[1278], DS137[1279], DS137[1280], DS137[1281], DS137[1282], DS137[1283], DS137[1284], DS137[1285], DS137[1286], DS137[1288], DS137[1289], DS137[1290], DS137[1291], DS137[1292], DS137[1293], DS137[1294], DS137[1295], DS137[1296], DS137[1297], DS137[1298], DS137[1299], DS137[1300], DS137[1301], DS137[1302], DS137[1303], DS137[1304], DS137[1305], DS137[1306], DS137[1307], DS137[1308], DS137[1309], DS137[1310], DS137[1312], DS137[1314], DS137[1315], DS137[1316], DS137[1317], DS137[1318], DS137[1319], DS137[1320], DS137[1321], DS137[1322], DS137[1323], DS137[1324], DS137[1325], DS137[1326], DS137[1328], DS137[1329], DS137[1330], DS137[1331], DS137[1332], DS137[1333], DS137[1334], DS137[1335], DS137[1336], DS137[1337], DS137[1338], DS137[1339], DS137[1340], DS137[1341], DS137[1342], DS137[1343], DS137[1347], DS137[1352], DS137[1356], DS137[1357], DS137[1358], DS137[1359], DS137[1360], DS137[1361], DS137[1362], DS137[1363], DS137[1364], DS137[1365], DS137[1366], DS137[1369], DS137[1370], DS137[1373], DS137[1374], DS137[1375], DS137[1376], DS137[1377], DS137[1378], DS137[1379], DS137[1380], DS137[1381], DS137[1382], DS137[1383], DS137[1384], DS137[1385], DS137[1386], DS137[1387], DS137[1388], DS137[1389], DS137[1390], DS137[1391], DS137[1392], DS137[1393], DS137[1394], DS137[1395], DS137[1396], DS137[1397], DS137[1398], DS137[1399], DS137[1400], DS137[1401], DS137[1402], DS137[1403], DS137[1404], DS137[1405], DS137[1406], DS137[1407], DS137[1408], DS137[1409], DS137[1410], DS137[1411], DS137[1412], DS137[1413], DS137[1414], DS137[1415], DS137[1416], DS137[1417], DS137[1418], DS137[1419], DS137[1420], DS137[1421], DS137[1422], DS137[1423], DS137[1424], DS137[1425], DS137[1426], DS137[1427], DS137[1428], DS137[1429], DS137[1430], DS137[1431], DS137[1432], DS137[1433], DS137[1434], DS137[1435], DS137[1436], DS137[1437], DS137[1438], DS137[1439], DS137[1440], DS137[1441], DS137[1442], DS137[1443], DS137[1444], DS137[1445], DS137[1446], DS137[1447], DS137[1448], DS137[1449], DS137[1450], DS137[1451], DS137[1452], DS137[1453], DS137[1454], DS137[1455], DS137[1456], DS137[1457], DS137[1458], DS137[1459], DS137[1460], DS137[1461], DS137[1462], DS137[1463], DS137[1464], DS137[1465], DS137[1466], DS137[1467], DS137[1468], DS137[1469], DS137[1470], DS137[1471], DS137[1472], DS137[1473], DS137[1474], DS137[1475], DS137[1476], DS137[1477], DS137[1478], DS137[1479], DS137[1480], DS137[1481], DS137[1482], DS137[1483], DS137[1484], DS137[1485], DS137[1486], DS137[1487], DS137[1488], DS137[1489], DS137[1490], DS137[1491], DS137[1492], DS137[1493], DS137[1494], DS137[1495], DS137[1496], DS137[1497], DS137[1498], DS137[1499], DS137[1500], DS137[1501], DS137[1502], DS137[1503], DS137[1504], DS137[1505], DS137[1506], DS137[1507], DS137[1508], DS137[1509], DS137[1510], DS137[1511], DS137[1512], DS137[1513], DS137[1514], DS137[1515], DS137[1516], DS137[1517], DS137[1518], DS137[1519], DS137[1520], DS137[1521], DS137[1522], DS137[1523], DS137[1524], DS137[1525], DS137[1526], DS137[1527], DS137[1528], DS137[1529], DS137[1530], DS137[1531], DS137[1532], DS137[1533], DS137[1534], DS137[1535], DS137[1536], DS137[1537], DS137[1538], DS137[1539], DS137[1540], DS137[1541], DS137[1542], DS137[1543], DS137[1544], DS137[1545], DS137[1546], DS137[1547], DS137[1548], DS137[1549], DS137[1550], DS137[1551], DS137[1552], DS137[1553], DS137[1554], DS137[1555], DS137[1556], DS137[1557], DS137[1558], DS137[1559], DS137[1560], DS137[1561], DS137[1562], DS137[1563], DS137[1564], DS137[1565], DS137[1566], DS137[1567], DS137[1568], DS137[1569], DS137[1570], DS137[1571], DS137[1572], DS137[1573], DS137[1574], DS137[1575], DS137[1576], DS137[1577], DS137[1578], DS137[1579], DS137[1580], DS137[1581], DS137[1582], DS137[1583], DS137[1584], DS137[1585], DS137[1586], DS137[1587], DS137[1588], DS137[1589], DS137[1590], DS137[1591], DS137[1592], DS137[1593], DS137[1594], DS137[1595], DS137[1596], DS137[1597], DS137[1598], DS137[1599], DS137[1600], DS137[1601], DS137[1602], DS137[1603], DS137[1604], DS137[1605], DS137[1606], DS137[1607], DS137[1608]. # Note that there is no reversible (64,28,12) difference sets in # group [64,137]. ########################### ########################### ###########################