### 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 [64,112]. 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 [64,112]. # 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(64,112));' can be # used to create a list e of the elements of the group [64,112]. # In our list of (64,28,12) DSs in group [64,112], we have [1, # 2, 3, 4, 5, 8, 9, 12, 14, 17, 18, 19, 25, 26, 28, # 30, 39, 40, 43, 44, 45, 48, 50, 52, 55, 62, 63, 64]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[8], e[9], e[12], e[14], e[17], e[18], e[19], e[25], e[26], e[28], e[30], # e[39], e[40], e[43], e[44], e[45], e[48], e[50], e[52], e[55], e[62], e[63], e[64]] # where e is the list of the elements of the group [64,112] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,112));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 112] ### The number of inequivalent (64,28,12) DSs in group [64,112] is 1186 ### The list of all inequivalent (64,28,12) DSs in group [64,112] is DS112:=[ [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 17, 18, 19, 25, 26, 28, 30, 39, 40, 43, 44, 45, 48, 50, 52, 55, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 17, 18, 19, 23, 25, 26, 28, 30, 39, 40, 48, 50, 52, 55, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 15, 16, 17, 23, 25, 26, 28, 30, 36, 37, 48, 50, 52, 55, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 17, 18, 19, 28, 29, 31, 39, 40, 43, 44, 46, 47, 48, 51, 52, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 17, 18, 19, 25, 26, 28, 31, 39, 40, 43, 44, 48, 50, 52, 55, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 17, 18, 19, 23, 28, 29, 31, 39, 40, 45, 46, 47, 48, 51, 52, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 17, 18, 19, 23, 25, 26, 28, 31, 39, 40, 45, 48, 50, 52, 55, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 15, 16, 17, 23, 28, 29, 31, 36, 37, 45, 46, 47, 48, 51, 52, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 15, 16, 17, 23, 25, 26, 28, 31, 36, 37, 45, 48, 50, 52, 55, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 32, 39, 40, 43, 44, 46, 47, 48, 49, 50, 51, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 26, 32, 39, 40, 43, 45, 46, 49, 50, 51, 55, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 26, 29, 39, 40, 43, 46, 48, 49, 51, 52, 55, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 26, 28, 32, 39, 40, 43, 44, 45, 46, 50, 55, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 26, 28, 29, 39, 40, 43, 44, 46, 48, 52, 55, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 25, 29, 39, 40, 43, 45, 47, 48, 49, 51, 52, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 25, 29, 32, 39, 40, 43, 45, 47, 49, 55, 58, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 19, 25, 28, 39, 40, 43, 44, 47, 48, 50, 51, 52, 55, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 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41, 45, 52, 56, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 20, 22, 26, 29, 34, 39, 41, 44, 45, 52, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 23, 29, 30, 31, 33, 39, 41, 46, 47, 53, 56, 57, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 23, 25, 29, 30, 31, 33, 39, 41, 47, 48, 53, 56, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 28, 34, 37, 38, 39, 40, 43, 45, 53, 56, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 28, 33, 36, 37, 40, 43, 44, 51, 54, 55, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 28, 33, 36, 37, 40, 41, 43, 44, 54, 56, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 25, 28, 33, 34, 37, 40, 41, 43, 48, 54, 55, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 25, 28, 33, 34, 37, 38, 40, 43, 51, 54, 55, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 23, 36, 37, 39, 40, 43, 44, 45, 55, 56, 57, 61, 62, 63 ], [ 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12, 16, 18, 19, 21, 23, 38, 39, 42, 43, 44, 45, 53, 55, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 18, 19, 21, 23, 34, 38, 39, 42, 43, 44, 45, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 21, 25, 35, 39, 42, 43, 46, 53, 54, 55, 57, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 21, 25, 34, 35, 39, 42, 43, 46, 54, 57, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 21, 25, 34, 35, 39, 41, 42, 43, 46, 51, 54, 55, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 21, 25, 28, 35, 36, 42, 43, 51, 53, 54, 55, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 21, 25, 28, 34, 35, 36, 42, 43, 51, 54, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 18, 21, 25, 35, 41, 42, 43, 46, 53, 54, 55, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 18, 21, 25, 34, 35, 41, 42, 43, 46, 54, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 26, 27, 28, 31, 33, 41, 45, 46, 52, 53, 55, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 26, 27, 28, 31, 33, 36, 41, 44, 45, 52, 55, 56, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 23, 29, 30, 31, 33, 41, 47, 48, 49, 53, 55, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 23, 29, 30, 31, 33, 38, 41, 47, 49, 53, 56, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 21, 22, 23, 28, 36, 37, 39, 40, 43, 45, 55, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 21, 23, 37, 38, 39, 40, 43, 44, 45, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 21, 23, 28, 34, 37, 38, 40, 41, 43, 45, 55, 57, 61, 64 ], [ 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, 35, 37, 38, 41, 43, 49, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 20, 21, 23, 37, 38, 40, 41, 43, 44, 45, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 19, 26, 30, 33, 41, 44, 47, 52, 58, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 21, 23, 36, 41, 42, 43, 44, 45, 53, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 21, 23, 36, 39, 41, 42, 43, 45, 49, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 21, 23, 34, 36, 41, 42, 43, 44, 45, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 34, 41, 43, 45, 49, 56, 57, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 21, 35, 36, 39, 41, 42, 43, 49, 54, 56, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 21, 28, 35, 36, 42, 43, 49, 53, 54, 55, 56, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 21, 28, 34, 35, 36, 42, 43, 49, 54, 56, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 21, 25, 28, 35, 39, 42, 43, 48, 53, 54, 55, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 21, 25, 28, 34, 35, 39, 42, 43, 48, 54, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 21, 35, 38, 39, 41, 42, 43, 49, 54, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 21, 28, 35, 38, 42, 43, 49, 53, 54, 55, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 21, 28, 34, 35, 38, 42, 43, 49, 54, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 29, 30, 31, 33, 35, 39, 44, 46, 48, 51, 55, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 29, 30, 31, 33, 34, 35, 46, 48, 49, 51, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 28, 29, 31, 33, 35, 39, 44, 48, 52, 55, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 28, 29, 30, 31, 33, 34, 35, 46, 48, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 25, 26, 29, 30, 31, 33, 35, 39, 51, 55, 56, 58, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 25, 26, 29, 30, 31, 33, 34, 35, 49, 51, 56, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 25, 26, 28, 29, 31, 33, 35, 39, 46, 52, 55, 56, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 25, 26, 28, 29, 30, 31, 33, 34, 35, 56, 57, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 25, 28, 35, 37, 40, 41, 43, 48, 53, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 25, 28, 35, 37, 38, 40, 43, 51, 53, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 20, 21, 28, 35, 37, 38, 40, 43, 44, 51, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 20, 21, 28, 35, 37, 38, 40, 41, 43, 44, 57, 60, 61, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 793 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS112[1], DS112[6], DS112[12], DS112[21], DS112[24], DS112[26], DS112[47], DS112[55], DS112[58], DS112[70], DS112[75], DS112[80], DS112[82], DS112[85], DS112[87], DS112[90], DS112[91], DS112[96], DS112[97], DS112[100], DS112[101], DS112[103], DS112[104], DS112[105], DS112[109], DS112[114], DS112[124], DS112[126], DS112[129], DS112[134], DS112[136], DS112[137], DS112[138], DS112[139], DS112[145], DS112[154], DS112[158], DS112[159], DS112[165], DS112[166], DS112[169], DS112[173], DS112[178], DS112[187], DS112[188], DS112[189], DS112[190], DS112[192], DS112[193], DS112[197], DS112[198], DS112[199], DS112[206], DS112[208], DS112[210], DS112[214], DS112[217], DS112[218], DS112[224], DS112[225], DS112[226], DS112[228], DS112[232], DS112[233], DS112[234], DS112[235], DS112[236], DS112[239], DS112[243], DS112[249], DS112[250], DS112[251], DS112[255], DS112[256], DS112[259], DS112[261], DS112[262], DS112[264], DS112[265], DS112[266], DS112[267], DS112[274], DS112[279], DS112[280], DS112[283], DS112[284], DS112[285], DS112[286], DS112[289], DS112[291], DS112[295], DS112[298], DS112[300], DS112[302], DS112[306], DS112[310], DS112[311], DS112[312], DS112[318], DS112[319], DS112[320], DS112[327], DS112[331], DS112[333], DS112[338], DS112[339], DS112[348], DS112[354], DS112[355], DS112[356], DS112[362], DS112[364], DS112[372], DS112[376], DS112[377], DS112[379], DS112[380], DS112[382], DS112[384], DS112[393], DS112[394], DS112[401], DS112[402], DS112[403], DS112[404], DS112[405], DS112[406], DS112[407], DS112[409], DS112[410], DS112[411], DS112[412], DS112[415], DS112[420], DS112[424], DS112[430], DS112[432], DS112[438], DS112[439], DS112[441], DS112[442], DS112[443], DS112[445], DS112[446], DS112[447], DS112[450], DS112[452], DS112[460], DS112[462], DS112[468], DS112[472], DS112[473], DS112[475], DS112[476], DS112[478], DS112[480], DS112[481], DS112[482], DS112[483], DS112[484], DS112[485], DS112[486], DS112[487], DS112[488], DS112[489], DS112[490], DS112[491], DS112[492], DS112[494], DS112[495], DS112[497], DS112[498], DS112[499], DS112[500], DS112[501], DS112[502], DS112[503], DS112[504], DS112[505], DS112[506], DS112[507], DS112[509], DS112[510], DS112[511], DS112[512], DS112[513], DS112[514], DS112[515], DS112[516], DS112[517], DS112[518], DS112[519], DS112[520], DS112[521], DS112[522], DS112[523], DS112[524], DS112[525], DS112[526], DS112[527], DS112[528], DS112[529], DS112[530], DS112[531], DS112[532], DS112[533], DS112[534], DS112[535], DS112[536], DS112[537], DS112[538], DS112[539], DS112[540], DS112[541], DS112[542], DS112[543], DS112[544], DS112[545], DS112[546], DS112[547], DS112[548], DS112[549], DS112[551], DS112[553], DS112[554], DS112[555], DS112[556], DS112[557], DS112[558], DS112[559], DS112[560], DS112[561], DS112[562], DS112[563], DS112[564], DS112[565], DS112[566], DS112[567], DS112[568], DS112[569], DS112[570], DS112[571], DS112[572], DS112[573], DS112[574], DS112[575], DS112[576], DS112[577], DS112[578], DS112[580], DS112[581], DS112[582], DS112[583], DS112[584], DS112[585], DS112[586], DS112[587], DS112[588], DS112[589], DS112[590], DS112[591], DS112[592], DS112[593], DS112[594], DS112[595], DS112[597], DS112[598], DS112[599], DS112[600], DS112[602], DS112[603], DS112[604], DS112[605], DS112[606], DS112[607], DS112[608], DS112[609], DS112[610], DS112[612], DS112[613], DS112[614], DS112[615], DS112[616], DS112[617], DS112[618], DS112[619], DS112[620], DS112[621], DS112[622], DS112[623], DS112[624], DS112[625], DS112[626], DS112[627], DS112[629], DS112[630], DS112[631], DS112[632], DS112[633], DS112[634], DS112[635], DS112[636], DS112[637], DS112[638], DS112[639], DS112[640], DS112[641], DS112[643], DS112[645], DS112[646], DS112[647], DS112[648], DS112[649], DS112[650], DS112[651], DS112[652], DS112[657], DS112[658], DS112[659], DS112[660], DS112[661], DS112[662], DS112[663], DS112[664], DS112[665], DS112[666], DS112[667], DS112[668], DS112[669], DS112[670], DS112[671], DS112[672], DS112[673], DS112[674], DS112[675], DS112[676], DS112[677], DS112[678], DS112[679], DS112[680], DS112[681], DS112[682], DS112[683], DS112[684], DS112[685], DS112[686], DS112[687], DS112[688], DS112[689], DS112[690], DS112[691], DS112[692], DS112[693], DS112[694], DS112[695], DS112[696], DS112[697], DS112[698], DS112[699], DS112[700], DS112[701], DS112[702], DS112[703], DS112[704], DS112[706], DS112[707], DS112[708], DS112[709], DS112[710], DS112[711], DS112[713], DS112[714], DS112[717], DS112[718], DS112[719], DS112[720], DS112[721], DS112[722], DS112[723], DS112[724], DS112[725], DS112[726], DS112[727], DS112[728], DS112[729], DS112[730], DS112[731], DS112[732], DS112[733], DS112[734], DS112[735], DS112[736], DS112[737], DS112[738], DS112[739], DS112[740], DS112[741], DS112[742], DS112[743], DS112[744], DS112[745], DS112[746], DS112[747], DS112[748], DS112[749], DS112[750], DS112[751], DS112[752], DS112[753], DS112[754], DS112[755], DS112[756], DS112[757], DS112[758], DS112[759], DS112[760], DS112[761], DS112[762], DS112[763], DS112[766], DS112[775], DS112[777], DS112[780], DS112[781], DS112[782], DS112[783], DS112[784], DS112[785], DS112[786], DS112[787], DS112[788], DS112[789], DS112[790], DS112[791], DS112[793], DS112[794], DS112[795], DS112[796], DS112[798], DS112[799], DS112[800], DS112[801], DS112[802], DS112[803], DS112[804], DS112[805], DS112[806], DS112[807], DS112[808], DS112[811], DS112[812], DS112[813], DS112[814], DS112[815], DS112[816], DS112[817], DS112[818], DS112[819], DS112[820], DS112[821], DS112[822], DS112[823], DS112[824], DS112[825], DS112[826], DS112[827], DS112[828], DS112[829], DS112[833], DS112[834], DS112[835], DS112[836], DS112[837], DS112[838], DS112[840], DS112[841], DS112[842], DS112[843], DS112[844], DS112[845], DS112[846], DS112[847], DS112[848], DS112[849], DS112[850], DS112[851], DS112[852], DS112[853], DS112[854], DS112[855], DS112[856], DS112[857], DS112[858], DS112[859], DS112[860], DS112[861], DS112[862], DS112[863], DS112[864], DS112[865], DS112[866], DS112[867], DS112[868], DS112[869], DS112[870], DS112[872], DS112[873], DS112[874], DS112[875], DS112[876], DS112[877], DS112[878], DS112[879], DS112[880], DS112[881], DS112[883], DS112[884], DS112[885], DS112[886], DS112[887], DS112[888], DS112[889], DS112[890], DS112[891], DS112[892], DS112[893], DS112[894], DS112[895], DS112[896], DS112[897], DS112[898], DS112[899], DS112[900], DS112[901], DS112[902], DS112[903], DS112[904], DS112[905], DS112[906], DS112[907], DS112[908], DS112[909], DS112[910], DS112[911], DS112[912], DS112[913], DS112[914], DS112[915], DS112[916], DS112[917], DS112[918], DS112[919], DS112[920], DS112[921], DS112[922], DS112[923], DS112[924], DS112[925], DS112[926], DS112[927], DS112[928], DS112[929], DS112[930], DS112[931], DS112[932], DS112[933], DS112[934], DS112[935], DS112[936], DS112[937], DS112[938], DS112[939], DS112[940], DS112[941], DS112[942], DS112[943], DS112[944], DS112[945], DS112[946], DS112[947], DS112[948], DS112[949], DS112[950], DS112[951], DS112[952], DS112[953], DS112[954], DS112[955], DS112[956], DS112[957], DS112[958], DS112[959], DS112[960], DS112[961], DS112[962], DS112[963], DS112[964], DS112[965], DS112[966], DS112[967], DS112[968], DS112[969], DS112[970], DS112[971], DS112[972], DS112[973], DS112[974], DS112[975], DS112[976], DS112[977], DS112[978], DS112[979], DS112[980], DS112[981], DS112[982], DS112[983], DS112[984], DS112[985], DS112[986], DS112[987], DS112[989], DS112[990], DS112[993], DS112[998], DS112[999], DS112[1001], DS112[1002], DS112[1003], DS112[1004], DS112[1005], DS112[1006], DS112[1007], DS112[1008], DS112[1009], DS112[1010], DS112[1011], DS112[1012], DS112[1013], DS112[1014], DS112[1015], DS112[1016], DS112[1017], DS112[1018], DS112[1019], DS112[1020], DS112[1021], DS112[1022], DS112[1023], DS112[1024], DS112[1025], DS112[1026], DS112[1027], DS112[1028], DS112[1029], DS112[1030], DS112[1031], DS112[1032], DS112[1033], DS112[1034], DS112[1035], DS112[1040], DS112[1041], DS112[1042], DS112[1043], DS112[1052], DS112[1053], DS112[1055], DS112[1058], DS112[1059], DS112[1060], DS112[1061], DS112[1062], DS112[1063], DS112[1064], DS112[1065], DS112[1066], DS112[1067], DS112[1068], DS112[1069], DS112[1070], DS112[1071], DS112[1072], DS112[1073], DS112[1074], DS112[1075], DS112[1076], DS112[1077], DS112[1078], DS112[1079], DS112[1081], DS112[1082], DS112[1083], DS112[1084], DS112[1085], DS112[1086], DS112[1087], DS112[1088], DS112[1089], DS112[1090], DS112[1091], DS112[1092], DS112[1093], DS112[1094], DS112[1095], DS112[1096], DS112[1097], DS112[1098], DS112[1099], DS112[1100], DS112[1101], DS112[1102], DS112[1103], DS112[1104], DS112[1105], DS112[1106], DS112[1107], DS112[1108], DS112[1109], DS112[1110], DS112[1111], DS112[1112], DS112[1113], DS112[1114], DS112[1115], DS112[1116], DS112[1119], DS112[1120], DS112[1121], DS112[1122], DS112[1123], DS112[1124], DS112[1125], DS112[1126], DS112[1127], DS112[1128], DS112[1129], DS112[1130], DS112[1131], DS112[1132], DS112[1133], DS112[1134], DS112[1135], DS112[1136], DS112[1137], DS112[1138], DS112[1139], DS112[1140], DS112[1141], DS112[1142], DS112[1143], DS112[1144], DS112[1145], DS112[1146], DS112[1147], DS112[1148], DS112[1149], DS112[1150], DS112[1151], DS112[1152], DS112[1153], DS112[1154], DS112[1155], DS112[1156], DS112[1157], DS112[1158], DS112[1159], DS112[1160], DS112[1161], DS112[1162], DS112[1163], DS112[1164], DS112[1165], DS112[1166], DS112[1167], DS112[1168], DS112[1169], DS112[1170], DS112[1171], DS112[1172], DS112[1173], DS112[1174], DS112[1175], DS112[1176], DS112[1177], DS112[1178], DS112[1179], DS112[1180], DS112[1181], DS112[1182], DS112[1183], DS112[1184], DS112[1185], DS112[1186]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,112]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,112] is 16 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,112] is RDS112:=[ [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 17, 21, 26, 28, 32, 33, 34, 43, 44, 45, 46, 50, 53, 55, 61, 62, 63, 64 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 17, 21, 23, 26, 28, 32, 33, 34, 46, 50, 53, 55, 58, 59, 60, 61, 62, 63 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 17, 18, 21, 26, 28, 32, 33, 39, 41, 43, 44, 45, 46, 50, 57, 61, 62, 64 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 17, 18, 21, 23, 26, 28, 32, 33, 39, 41, 46, 50, 57, 58, 59, 60, 61, 62 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 15, 17, 21, 26, 28, 32, 33, 36, 38, 43, 44, 45, 46, 50, 56, 61, 62, 64 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 15, 17, 21, 23, 26, 28, 32, 33, 36, 38, 46, 50, 56, 58, 59, 60, 61, 62 ], [ 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 17, 20, 21, 22, 26, 28, 32, 33, 42, 43, 44, 45, 46, 50, 61, 62, 64 ], [ 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 17, 20, 21, 22, 23, 26, 28, 32, 33, 42, 46, 50, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 26, 28, 32, 34, 35, 43, 44, 45, 46, 50, 53, 54, 55, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 23, 26, 28, 32, 34, 35, 46, 50, 53, 54, 55, 58, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 26, 28, 32, 35, 39, 41, 43, 44, 45, 46, 50, 54, 57, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 17, 18, 23, 26, 28, 32, 35, 39, 41, 46, 50, 54, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 17, 26, 28, 32, 35, 36, 38, 43, 44, 45, 46, 50, 54, 56, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 17, 23, 26, 28, 32, 35, 36, 38, 46, 50, 54, 56, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 17, 20, 22, 26, 28, 32, 35, 42, 43, 44, 45, 46, 50, 54, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 17, 20, 22, 23, 26, 28, 32, 35, 42, 46, 50, 54, 58, 59, 60, 61, 62 ] ]; ########################### ########################### ###########################