### 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 [64,116]. 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 [64,116]. # 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(64,116));' can be # used to create a list e of the elements of the group [64,116]. # In our list of (64,28,12) DSs in group [64,116], we have [1, # 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 18, 22, 23, 29, # 31, 38, 40, 43, 44, 49, 53, 54, 55, 56, 57, 58, 62]. # 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[18], e[22], e[23], e[29], e[31], # e[38], e[40], e[43], e[44], e[49], e[53], e[54], e[55], e[56], e[57], e[58], e[62]] # where e is the list of the elements of the group [64,116] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,116));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 116] ### The number of inequivalent (64,28,12) DSs in group [64,116] is 2364 ### The list of all inequivalent (64,28,12) DSs in group [64,116] is DS116:=[ [ 1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 18, 22, 23, 29, 31, 38, 40, 43, 44, 49, 53, 54, 55, 56, 57, 58, 62 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 18, 22, 23, 29, 31, 36, 40, 43, 49, 53, 54, 55, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 11, 13, 16, 17, 18, 22, 30, 36, 39, 44, 46, 47, 48, 53, 54, 55, 56, 58, 60, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 11, 13, 16, 17, 18, 22, 25, 30, 34, 36, 39, 44, 47, 54, 56, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 11, 13, 16, 17, 18, 22, 23, 30, 36, 39, 43, 45, 46, 47, 48, 53, 54, 55, 56, 59 ], [ 1, 2, 3, 4, 6, 7, 8, 10, 11, 13, 16, 17, 18, 22, 23, 25, 30, 34, 36, 39, 43, 45, 47, 54, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 13, 16, 22, 24, 27, 29, 30, 31, 32, 33, 36, 39, 40, 41, 48, 50, 55, 56, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 13, 16, 22, 24, 25, 27, 29, 30, 31, 32, 33, 34, 36, 39, 40, 41, 46, 50, 53, 56 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 14, 17, 19, 22, 23, 29, 31, 38, 40, 43, 44, 46, 47, 48, 49, 52, 56, 58, 62 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 14, 15, 17, 19, 22, 23, 29, 31, 36, 40, 43, 46, 47, 48, 49, 52, 60, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 16, 18, 22, 24, 27, 29, 31, 33, 36, 40, 48, 50, 52, 55, 56, 57, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 16, 18, 22, 24, 25, 27, 29, 31, 33, 34, 36, 40, 46, 50, 52, 53, 56, 57 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 20, 22, 24, 29, 34, 35, 37, 39, 40, 42, 43, 45, 48, 52, 53, 54, 57, 61 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 20, 22, 24, 25, 29, 35, 37, 39, 40, 42, 43, 45, 46, 52, 54, 55, 57, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 20, 22, 24, 29, 33, 37, 39, 40, 42, 43, 45, 48, 52, 55, 57, 61, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 20, 22, 24, 25, 29, 33, 34, 37, 39, 40, 42, 43, 45, 46, 52, 53, 57 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 19, 22, 23, 31, 34, 35, 36, 37, 38, 39, 42, 43, 44, 49, 50, 51, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 18, 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9, 10, 11, 16, 18, 19, 31, 32, 34, 37, 38, 40, 45, 52, 53, 54, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 18, 19, 25, 31, 37, 38, 40, 41, 45, 46, 54, 57, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 21, 24, 28, 29, 34, 35, 36, 42, 43, 45, 51, 52, 54, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 21, 23, 24, 28, 29, 35, 36, 42, 51, 52, 53, 54, 55, 56, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 30, 31, 33, 34, 37, 44, 46, 51, 52, 53, 55, 56, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 26, 28, 29, 31, 36, 38, 45, 47, 49, 50, 54, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 26, 27, 28, 31, 36, 38, 43, 47, 50, 51, 54, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 23, 26, 31, 36, 38, 43, 45, 47, 54, 58, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 23, 26, 27, 29, 30, 31, 32, 33, 35, 47, 54, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 20, 22, 23, 26, 27, 29, 31, 47, 54, 58, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 17, 21, 22, 24, 29, 32, 35, 37, 39, 43, 44, 45, 54, 56, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 17, 21, 22, 23, 24, 29, 32, 35, 37, 39, 54, 56, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 17, 18, 21, 23, 26, 30, 33, 37, 38, 39, 42, 45, 50, 54, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 17, 18, 21, 23, 26, 30, 33, 37, 38, 39, 42, 44, 45, 50, 54, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 21, 24, 29, 34, 35, 38, 42, 43, 45, 49, 52, 54, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 21, 23, 24, 29, 35, 38, 42, 49, 52, 53, 54, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 23, 29, 31, 33, 37, 38, 46, 49, 50, 53, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 22, 23, 31, 33, 37, 42, 45, 46, 49, 53, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 21, 22, 23, 29, 32, 33, 35, 38, 39, 44, 47, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 20, 21, 24, 29, 34, 35, 37, 38, 40, 43, 45, 49, 52, 55, 56, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 20, 21, 24, 28, 29, 35, 37, 38, 40, 43, 45, 51, 52, 53, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 23, 26, 30, 31, 36, 40, 41, 43, 45, 47, 51, 52, 53, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 25, 26, 30, 33, 34, 37, 39, 42, 48, 50, 53, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 25, 26, 30, 33, 34, 37, 39, 42, 44, 48, 50, 53, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 24, 30, 34, 35, 37, 39, 42, 48, 50, 55, 57, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 24, 30, 34, 35, 37, 39, 42, 44, 48, 50, 55, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 26, 28, 29, 30, 31, 35, 36, 45, 47, 50, 52, 54, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 19, 21, 26, 30, 33, 34, 37, 41, 42, 46, 50, 53, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 19, 21, 26, 30, 33, 34, 37, 41, 42, 44, 46, 50, 53, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 19, 21, 24, 30, 35, 37, 41, 42, 48, 50, 53, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 19, 21, 24, 30, 35, 37, 41, 42, 44, 48, 50, 53, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 21, 22, 23, 29, 32, 36, 37, 38, 39, 43, 44, 47, 54, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 18, 21, 26, 30, 34, 35, 37, 39, 42, 46, 50, 55, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 18, 21, 26, 30, 34, 35, 37, 39, 42, 44, 46, 50, 55, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 18, 21, 25, 26, 30, 35, 37, 39, 42, 48, 50, 53, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 18, 21, 25, 26, 30, 35, 37, 39, 42, 44, 48, 50, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 21, 22, 24, 27, 35, 36, 38, 39, 40, 44, 45, 52, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 20, 25, 27, 31, 33, 37, 38, 39, 42, 44, 45, 50, 51, 53, 54 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 31, 32, 33, 37, 38, 41, 45, 52, 54, 57, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 30, 31, 32, 33, 37, 38, 39, 41, 45, 46, 53, 54, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 25, 31, 33, 34, 37, 38, 45, 46, 53, 54, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 31, 32, 34, 37, 38, 40, 45, 52, 55, 57, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 30, 31, 32, 34, 37, 38, 39, 40, 45, 46, 53, 55, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 25, 31, 34, 37, 38, 39, 40, 45, 46, 57, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 20, 25, 31, 34, 37, 38, 40, 42, 43, 45, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 18, 21, 26, 30, 35, 37, 38, 39, 42, 43, 50, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 18, 21, 26, 30, 35, 37, 38, 39, 42, 43, 44, 50, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 21, 22, 24, 27, 35, 39, 40, 45, 52, 56, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 27, 29, 31, 34, 37, 38, 39, 40, 45, 46, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 26, 30, 34, 35, 39, 40, 41, 42, 44, 46, 50, 55, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 25, 26, 30, 35, 39, 40, 41, 42, 44, 48, 50, 53, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 21, 22, 23, 29, 32, 38, 39, 44, 47, 54, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 21, 26, 30, 35, 38, 39, 40, 41, 42, 43, 50, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 21, 26, 30, 35, 38, 39, 40, 41, 42, 43, 44, 50, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 24, 30, 31, 39, 40, 46, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 24, 25, 30, 31, 39, 40, 44, 45, 48, 53, 55, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 27, 33, 36, 37, 39, 42, 44, 49, 53, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 26, 28, 29, 36, 39, 42, 44, 47, 48, 50, 54, 55, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 23, 26, 28, 36, 39, 42, 43, 47, 48, 51, 54, 55, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 23, 26, 27, 36, 39, 42, 44, 47, 48, 50, 54, 55, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 24, 30, 31, 40, 41, 44, 45, 46, 53, 55, 56, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 24, 25, 30, 31, 40, 41, 48, 53, 55, 56, 58, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 20, 22, 26, 27, 36, 43, 44, 47, 50, 54, 55, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 23, 26, 30, 32, 36, 39, 40, 43, 47, 51, 54, 55, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 21, 25, 27, 28, 33, 39, 42, 44, 45, 46, 51, 53, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 19, 30, 37, 38, 40, 41, 44, 46, 52, 53, 54, 55, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 21, 27, 28, 33, 37, 38, 39, 42, 44, 51, 53, 55, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 26, 27, 29, 30, 33, 35, 43, 47, 52, 54, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 23, 26, 27, 32, 35, 36, 41, 46, 47, 50, 52, 53, 54, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 21, 29, 33, 35, 36, 37, 39, 42, 45, 51, 55, 56, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 21, 23, 28, 29, 33, 35, 36, 37, 39, 42, 43, 49, 55, 56, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 23, 26, 27, 36, 40, 41, 46, 47, 48, 50, 53, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 23, 26, 27, 30, 32, 35, 36, 47, 50, 54, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 21, 25, 27, 34, 39, 42, 45, 46, 49, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 30, 33, 37, 38, 39, 41, 44, 46, 52, 53, 54, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 30, 34, 37, 38, 39, 40, 44, 46, 52, 53, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 23, 28, 29, 36, 37, 38, 39, 40, 46, 50, 53, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 22, 23, 28, 36, 37, 39, 40, 42, 45, 46, 53, 59, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1142 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS116[14], DS116[20], DS116[34], DS116[37], DS116[39], DS116[48], DS116[50], DS116[51], DS116[65], DS116[81], DS116[82], DS116[83], DS116[84], DS116[85], DS116[86], DS116[87], DS116[88], DS116[91], DS116[92], DS116[95], DS116[99], DS116[103], DS116[106], DS116[107], DS116[108], DS116[115], DS116[116], DS116[117], DS116[118], DS116[119], DS116[120], DS116[121], DS116[125], DS116[126], DS116[127], DS116[128], DS116[141], DS116[158], DS116[160], DS116[161], DS116[164], DS116[165], DS116[166], DS116[168], DS116[174], DS116[184], DS116[188], DS116[192], DS116[202], DS116[203], DS116[204], DS116[205], DS116[209], DS116[232], DS116[240], DS116[249], DS116[253], DS116[257], DS116[279], DS116[282], DS116[284], DS116[294], DS116[340], DS116[351], DS116[352], DS116[356], DS116[358], DS116[373], DS116[374], DS116[375], DS116[381], DS116[385], DS116[398], DS116[400], DS116[401], DS116[417], DS116[424], DS116[427], DS116[428], DS116[430], DS116[439], DS116[440], DS116[455], DS116[457], DS116[458], DS116[460], DS116[462], DS116[463], DS116[464], DS116[471], DS116[477], DS116[478], DS116[481], DS116[483], DS116[491], DS116[493], DS116[510], DS116[512], DS116[513], DS116[517], DS116[518], DS116[519], DS116[520], DS116[521], DS116[522], DS116[523], DS116[525], DS116[527], DS116[529], DS116[537], DS116[552], DS116[553], DS116[556], DS116[557], DS116[558], DS116[568], DS116[569], DS116[570], DS116[571], DS116[572], DS116[573], DS116[574], DS116[575], DS116[576], DS116[577], DS116[585], DS116[586], DS116[589], DS116[592], DS116[593], DS116[595], DS116[597], DS116[599], DS116[600], DS116[603], DS116[604], DS116[609], DS116[620], DS116[626], DS116[628], DS116[629], DS116[631], DS116[633], DS116[634], DS116[641], DS116[644], DS116[652], DS116[654], DS116[655], DS116[656], DS116[657], DS116[661], DS116[662], DS116[663], DS116[664], DS116[668], DS116[669], DS116[670], DS116[671], DS116[672], DS116[678], DS116[680], DS116[689], DS116[690], DS116[701], DS116[702], DS116[705], DS116[706], DS116[708], DS116[714], DS116[715], DS116[717], DS116[719], DS116[720], DS116[721], DS116[722], DS116[723], DS116[729], DS116[731], DS116[732], DS116[735], DS116[736], DS116[742], DS116[748], DS116[763], DS116[765], DS116[771], DS116[773], DS116[774], DS116[775], DS116[782], DS116[784], DS116[787], DS116[788], DS116[790], DS116[791], DS116[796], DS116[797], DS116[798], DS116[799], DS116[800], DS116[801], DS116[802], DS116[803], DS116[804], DS116[807], DS116[809], DS116[810], DS116[819], DS116[821], DS116[837], DS116[838], DS116[839], DS116[851], DS116[854], DS116[856], DS116[861], DS116[865], DS116[866], DS116[877], DS116[878], DS116[880], DS116[895], DS116[901], DS116[906], DS116[911], DS116[913], DS116[916], DS116[920], DS116[921], DS116[923], DS116[931], DS116[946], DS116[949], DS116[950], DS116[951], DS116[952], DS116[953], DS116[954], DS116[955], DS116[956], DS116[958], DS116[964], DS116[971], DS116[981], DS116[985], DS116[988], DS116[989], DS116[990], DS116[992], DS116[993], DS116[994], DS116[995], DS116[1012], DS116[1013], DS116[1032], DS116[1042], DS116[1043], DS116[1044], DS116[1049], DS116[1051], DS116[1057], DS116[1069], DS116[1072], DS116[1073], DS116[1078], DS116[1080], DS116[1081], DS116[1083], DS116[1087], DS116[1088], DS116[1089], DS116[1094], DS116[1096], DS116[1097], DS116[1100], DS116[1102], DS116[1105], DS116[1106], DS116[1107], DS116[1108], DS116[1109], DS116[1113], DS116[1114], DS116[1117], DS116[1118], DS116[1121], DS116[1122], DS116[1124], DS116[1125], DS116[1128], DS116[1130], DS116[1131], DS116[1132], DS116[1135], DS116[1136], DS116[1137], DS116[1139], DS116[1140], DS116[1141], DS116[1142], DS116[1143], DS116[1146], DS116[1147], DS116[1148], DS116[1153], DS116[1154], DS116[1155], DS116[1156], DS116[1158], DS116[1159], DS116[1160], DS116[1164], DS116[1166], DS116[1169], DS116[1170], DS116[1176], DS116[1181], DS116[1187], DS116[1191], DS116[1192], DS116[1208], DS116[1209], DS116[1235], DS116[1236], DS116[1237], DS116[1238], DS116[1239], DS116[1242], DS116[1243], DS116[1247], DS116[1248], DS116[1250], DS116[1264], DS116[1267], DS116[1269], DS116[1270], DS116[1271], DS116[1272], DS116[1275], DS116[1277], DS116[1278], DS116[1281], DS116[1282], DS116[1283], DS116[1288], DS116[1292], DS116[1293], DS116[1294], DS116[1297], DS116[1298], DS116[1299], DS116[1300], DS116[1301], DS116[1302], DS116[1303], DS116[1304], DS116[1306], DS116[1307], DS116[1308], DS116[1309], DS116[1310], DS116[1314], DS116[1315], DS116[1316], DS116[1317], DS116[1318], DS116[1319], DS116[1320], DS116[1322], DS116[1324], DS116[1325], DS116[1326], DS116[1328], DS116[1330], DS116[1331], DS116[1334], DS116[1335], DS116[1336], DS116[1339], DS116[1340], DS116[1341], DS116[1342], DS116[1343], DS116[1344], DS116[1345], DS116[1346], DS116[1347], DS116[1348], DS116[1349], DS116[1350], DS116[1351], DS116[1352], DS116[1353], DS116[1354], DS116[1355], DS116[1360], DS116[1361], DS116[1362], DS116[1363], DS116[1364], DS116[1365], DS116[1366], DS116[1367], DS116[1368], DS116[1369], DS116[1370], DS116[1371], DS116[1372], DS116[1373], DS116[1374], DS116[1375], DS116[1376], DS116[1377], DS116[1378], DS116[1379], DS116[1380], DS116[1381], DS116[1382], DS116[1383], DS116[1384], DS116[1385], DS116[1386], DS116[1387], DS116[1388], DS116[1389], DS116[1390], DS116[1391], DS116[1392], DS116[1393], DS116[1394], DS116[1395], DS116[1396], DS116[1397], DS116[1398], DS116[1400], DS116[1401], DS116[1402], DS116[1405], DS116[1406], DS116[1407], DS116[1408], DS116[1409], DS116[1410], DS116[1411], DS116[1412], DS116[1413], DS116[1414], DS116[1416], DS116[1425], DS116[1426], DS116[1427], DS116[1437], DS116[1446], DS116[1447], DS116[1450], DS116[1452], DS116[1453], DS116[1455], DS116[1477], DS116[1478], DS116[1479], DS116[1490], DS116[1491], DS116[1492], DS116[1493], DS116[1494], DS116[1496], DS116[1497], DS116[1498], DS116[1499], DS116[1500], DS116[1501], DS116[1502], DS116[1503], DS116[1504], DS116[1505], DS116[1506], DS116[1507], DS116[1508], DS116[1509], DS116[1510], DS116[1511], DS116[1512], DS116[1513], DS116[1514], DS116[1515], DS116[1516], DS116[1517], DS116[1521], DS116[1527], DS116[1529], DS116[1530], DS116[1531], DS116[1532], DS116[1533], DS116[1534], DS116[1535], DS116[1537], DS116[1538], DS116[1539], DS116[1540], DS116[1543], DS116[1547], DS116[1548], DS116[1550], DS116[1551], DS116[1554], DS116[1561], DS116[1568], DS116[1571], DS116[1572], DS116[1573], DS116[1574], DS116[1577], DS116[1578], DS116[1579], DS116[1580], DS116[1583], DS116[1584], DS116[1585], DS116[1586], DS116[1587], DS116[1590], DS116[1591], DS116[1594], DS116[1595], DS116[1596], DS116[1597], DS116[1598], DS116[1599], DS116[1600], DS116[1601], DS116[1602], DS116[1603], DS116[1607], DS116[1608], DS116[1609], DS116[1610], DS116[1617], DS116[1618], DS116[1619], DS116[1620], DS116[1621], DS116[1622], DS116[1623], DS116[1624], DS116[1625], DS116[1626], DS116[1627], DS116[1628], DS116[1629], DS116[1630], DS116[1631], DS116[1632], DS116[1633], DS116[1634], DS116[1635], DS116[1636], DS116[1637], DS116[1638], DS116[1639], DS116[1640], DS116[1641], DS116[1642], DS116[1647], DS116[1648], DS116[1650], DS116[1651], DS116[1652], DS116[1653], DS116[1654], DS116[1656], DS116[1657], DS116[1658], DS116[1659], DS116[1660], DS116[1661], DS116[1662], DS116[1663], DS116[1664], DS116[1665], DS116[1666], DS116[1667], DS116[1668], DS116[1669], DS116[1670], DS116[1671], DS116[1673], DS116[1674], DS116[1675], DS116[1677], DS116[1678], DS116[1679], DS116[1680], DS116[1683], DS116[1684], DS116[1685], DS116[1686], DS116[1687], DS116[1688], DS116[1689], DS116[1690], DS116[1691], DS116[1692], DS116[1693], DS116[1694], DS116[1695], DS116[1696], DS116[1698], DS116[1699], DS116[1700], DS116[1701], DS116[1702], DS116[1703], DS116[1705], DS116[1706], DS116[1707], DS116[1708], DS116[1709], DS116[1710], DS116[1711], DS116[1712], DS116[1713], DS116[1714], DS116[1715], DS116[1716], DS116[1717], DS116[1718], DS116[1719], DS116[1720], DS116[1721], DS116[1722], DS116[1723], DS116[1724], DS116[1725], DS116[1726], DS116[1727], DS116[1728], DS116[1729], DS116[1730], DS116[1731], DS116[1732], DS116[1733], DS116[1734], DS116[1735], DS116[1736], DS116[1737], DS116[1738], DS116[1739], DS116[1740], DS116[1741], DS116[1742], DS116[1744], DS116[1745], DS116[1746], DS116[1747], DS116[1748], DS116[1749], DS116[1750], DS116[1751], DS116[1752], DS116[1754], DS116[1755], DS116[1756], DS116[1757], DS116[1758], DS116[1760], DS116[1764], DS116[1766], DS116[1767], DS116[1768], DS116[1769], DS116[1772], DS116[1773], DS116[1775], DS116[1776], DS116[1778], DS116[1781], DS116[1782], DS116[1784], DS116[1785], DS116[1787], DS116[1788], DS116[1789], DS116[1790], DS116[1791], DS116[1792], DS116[1793], DS116[1794], DS116[1795], DS116[1796], DS116[1797], DS116[1802], DS116[1803], DS116[1804], DS116[1805], DS116[1806], DS116[1807], DS116[1808], DS116[1809], DS116[1810], DS116[1811], DS116[1812], DS116[1813], DS116[1814], DS116[1815], DS116[1816], DS116[1817], DS116[1818], DS116[1819], DS116[1820], DS116[1821], DS116[1822], DS116[1823], DS116[1824], DS116[1825], DS116[1826], DS116[1827], DS116[1828], DS116[1829], DS116[1830], DS116[1831], DS116[1832], DS116[1833], DS116[1834], DS116[1835], DS116[1836], DS116[1837], DS116[1838], DS116[1839], DS116[1840], DS116[1841], DS116[1842], DS116[1843], DS116[1844], DS116[1846], DS116[1852], DS116[1855], DS116[1857], DS116[1858], DS116[1859], DS116[1860], DS116[1861], DS116[1862], DS116[1865], DS116[1867], DS116[1868], DS116[1869], DS116[1870], DS116[1871], DS116[1872], DS116[1873], DS116[1874], DS116[1875], DS116[1876], DS116[1877], DS116[1878], DS116[1879], DS116[1880], DS116[1881], DS116[1882], DS116[1883], DS116[1886], DS116[1891], DS116[1892], DS116[1893], DS116[1894], DS116[1895], DS116[1896], DS116[1897], DS116[1898], DS116[1899], DS116[1900], DS116[1901], DS116[1902], DS116[1903], DS116[1904], DS116[1911], DS116[1917], DS116[1918], DS116[1920], DS116[1921], DS116[1922], DS116[1923], DS116[1924], DS116[1925], DS116[1926], DS116[1927], DS116[1928], DS116[1929], DS116[1930], DS116[1931], DS116[1932], DS116[1933], DS116[1934], DS116[1935], DS116[1936], DS116[1937], DS116[1938], DS116[1939], DS116[1940], DS116[1941], DS116[1942], DS116[1943], DS116[1944], DS116[1945], DS116[1946], DS116[1947], DS116[1948], DS116[1949], DS116[1950], DS116[1951], DS116[1952], DS116[1953], DS116[1954], DS116[1955], DS116[1956], DS116[1957], DS116[1958], DS116[1959], DS116[1960], DS116[1961], DS116[1962], DS116[1963], DS116[1964], DS116[1965], DS116[1966], DS116[1968], DS116[1969], DS116[1970], DS116[1971], DS116[1972], DS116[1973], DS116[1974], DS116[1975], DS116[1976], DS116[1977], DS116[1978], DS116[1979], DS116[1980], DS116[1981], DS116[1982], DS116[1983], DS116[1984], DS116[1985], DS116[1986], DS116[1987], DS116[1988], DS116[1989], DS116[1990], DS116[1991], DS116[1992], DS116[1993], DS116[1994], DS116[1995], DS116[1997], DS116[1998], DS116[1999], DS116[2000], DS116[2001], DS116[2002], DS116[2003], DS116[2004], DS116[2005], DS116[2006], DS116[2007], DS116[2009], DS116[2011], DS116[2014], DS116[2018], DS116[2019], DS116[2020], DS116[2021], DS116[2022], DS116[2023], DS116[2026], DS116[2027], DS116[2028], DS116[2029], DS116[2032], DS116[2033], DS116[2034], DS116[2035], DS116[2036], DS116[2037], DS116[2038], DS116[2039], DS116[2040], DS116[2041], DS116[2042], DS116[2043], DS116[2048], DS116[2049], DS116[2052], DS116[2057], DS116[2058], DS116[2059], DS116[2060], DS116[2065], DS116[2066], DS116[2067], DS116[2068], DS116[2069], DS116[2070], DS116[2071], DS116[2072], DS116[2073], DS116[2074], DS116[2075], DS116[2079], DS116[2084], DS116[2085], DS116[2086], DS116[2087], DS116[2088], DS116[2089], DS116[2090], DS116[2091], DS116[2092], DS116[2094], DS116[2095], DS116[2096], DS116[2097], DS116[2098], DS116[2099], DS116[2100], DS116[2103], DS116[2104], DS116[2109], DS116[2110], DS116[2111], DS116[2112], DS116[2113], DS116[2114], DS116[2115], DS116[2116], DS116[2117], DS116[2118], DS116[2119], DS116[2120], DS116[2121], DS116[2122], DS116[2124], DS116[2125], DS116[2126], DS116[2127], DS116[2128], DS116[2129], DS116[2130], DS116[2131], DS116[2132], DS116[2133], DS116[2134], DS116[2135], DS116[2136], DS116[2137], DS116[2138], DS116[2139], DS116[2140], DS116[2141], DS116[2142], DS116[2143], DS116[2144], DS116[2145], DS116[2146], DS116[2147], DS116[2148], DS116[2149], DS116[2150], DS116[2154], DS116[2155], DS116[2156], DS116[2157], DS116[2158], DS116[2159], DS116[2160], DS116[2161], DS116[2166], DS116[2167], DS116[2168], DS116[2169], DS116[2174], DS116[2175], DS116[2176], DS116[2177], DS116[2178], DS116[2179], DS116[2180], DS116[2181], DS116[2182], DS116[2183], DS116[2184], DS116[2185], DS116[2186], DS116[2187], DS116[2188], DS116[2189], DS116[2190], DS116[2191], DS116[2192], DS116[2193], DS116[2194], DS116[2195], DS116[2196], DS116[2197], DS116[2199], DS116[2200], DS116[2201], DS116[2202], DS116[2203], DS116[2204], DS116[2205], DS116[2206], DS116[2207], DS116[2208], DS116[2209], DS116[2210], DS116[2211], DS116[2212], DS116[2213], DS116[2214], DS116[2215], DS116[2216], DS116[2217], DS116[2218], DS116[2219], DS116[2220], DS116[2221], DS116[2222], DS116[2223], DS116[2224], DS116[2225], DS116[2226], DS116[2227], DS116[2228], DS116[2229], DS116[2230], DS116[2231], DS116[2232], DS116[2233], DS116[2234], DS116[2235], DS116[2236], DS116[2237], DS116[2238], DS116[2239], DS116[2240], DS116[2241], DS116[2242], DS116[2243], DS116[2244], DS116[2245], DS116[2246], DS116[2247], DS116[2248], DS116[2249], DS116[2250], DS116[2251], DS116[2252], DS116[2253], DS116[2254], DS116[2255], DS116[2258], DS116[2259], DS116[2260], DS116[2261], DS116[2262], DS116[2263], DS116[2266], DS116[2267], DS116[2268], DS116[2269], DS116[2271], DS116[2273], DS116[2276], DS116[2279], DS116[2282], DS116[2283], DS116[2285], DS116[2286], DS116[2287], DS116[2288], DS116[2290], DS116[2291], DS116[2292], DS116[2293], DS116[2294], DS116[2295], DS116[2296], DS116[2297], DS116[2298], DS116[2300], DS116[2301], DS116[2303], DS116[2304], DS116[2305], DS116[2306], DS116[2307], DS116[2308], DS116[2311], DS116[2313], DS116[2318], DS116[2323], DS116[2324], DS116[2325], DS116[2326], DS116[2327], DS116[2328], DS116[2329], DS116[2330], DS116[2331], DS116[2333], DS116[2334], DS116[2335], DS116[2338], DS116[2339], DS116[2340], DS116[2341], DS116[2342], DS116[2343], DS116[2344], DS116[2345], DS116[2346], DS116[2347], DS116[2348], DS116[2349], DS116[2350], DS116[2351], DS116[2352], DS116[2353], DS116[2354], DS116[2355], DS116[2356], DS116[2357], DS116[2358], DS116[2359], DS116[2360], DS116[2361], DS116[2362], DS116[2363], DS116[2364]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,116]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,116] is 120 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,116] is RDS116:=[ [ 2, 4, 5, 8, 9, 20, 21, 24, 29, 30, 31, 32, 34, 35, 39, 40, 41, 42, 44, 48, 49, 53, 54, 58, 60, 61, 62, 64 ], [ 2, 4, 5, 8, 9, 20, 21, 23, 24, 29, 30, 31, 32, 34, 35, 39, 40, 41, 42, 43, 45, 48, 49, 53, 54, 59, 61, 62 ], [ 2, 4, 5, 8, 9, 15, 20, 21, 24, 29, 30, 31, 32, 34, 35, 36, 38, 39, 40, 41, 42, 48, 49, 53, 54, 56, 61, 62 ], [ 2, 4, 5, 8, 9, 13, 20, 21, 24, 29, 30, 31, 32, 33, 39, 40, 41, 42, 44, 48, 49, 55, 58, 60, 61, 62, 63, 64 ], [ 2, 4, 5, 8, 9, 13, 20, 21, 23, 24, 29, 30, 31, 32, 33, 39, 40, 41, 42, 43, 45, 48, 49, 55, 59, 61, 62, 63 ], [ 2, 4, 5, 8, 9, 13, 15, 20, 21, 24, 29, 30, 31, 32, 33, 36, 38, 39, 40, 41, 42, 48, 49, 55, 56, 61, 62, 63 ], [ 2, 4, 5, 8, 9, 10, 13, 20, 21, 25, 29, 32, 33, 39, 40, 41, 42, 44, 47, 49, 52, 55, 58, 60, 61, 62, 63, 64 ], [ 2, 4, 5, 8, 9, 10, 13, 20, 21, 23, 25, 29, 32, 33, 39, 40, 41, 42, 43, 45, 47, 49, 52, 55, 59, 61, 62, 63 ], [ 2, 4, 5, 8, 9, 10, 13, 15, 20, 21, 25, 29, 32, 33, 36, 38, 39, 40, 41, 42, 47, 49, 52, 55, 56, 61, 62, 63 ], [ 2, 4, 5, 6, 8, 9, 21, 22, 24, 28, 29, 30, 31, 32, 34, 35, 39, 40, 41, 44, 48, 51, 53, 54, 58, 60, 61, 64 ], [ 2, 4, 5, 6, 8, 9, 21, 22, 23, 24, 28, 29, 30, 31, 32, 34, 35, 39, 40, 41, 43, 45, 48, 51, 53, 54, 59, 61 ], [ 2, 4, 5, 6, 8, 9, 15, 21, 22, 24, 28, 29, 30, 31, 32, 34, 35, 36, 38, 39, 40, 41, 48, 51, 53, 54, 56, 61 ], [ 2, 4, 5, 6, 8, 9, 13, 21, 22, 24, 28, 29, 30, 31, 32, 33, 39, 40, 41, 44, 48, 51, 55, 58, 60, 61, 63, 64 ], [ 2, 4, 5, 6, 8, 9, 13, 21, 22, 23, 24, 28, 29, 30, 31, 32, 33, 39, 40, 41, 43, 45, 48, 51, 55, 59, 61, 63 ], [ 2, 4, 5, 6, 8, 9, 13, 15, 21, 22, 24, 28, 29, 30, 31, 32, 33, 36, 38, 39, 40, 41, 48, 51, 55, 56, 61, 63 ], [ 2, 4, 5, 6, 8, 9, 10, 13, 21, 22, 25, 28, 29, 32, 33, 39, 40, 41, 44, 47, 51, 52, 55, 58, 60, 61, 63, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 13, 21, 22, 23, 25, 28, 29, 32, 33, 39, 40, 41, 43, 45, 47, 51, 52, 55, 59, 61, 63 ], [ 2, 4, 5, 6, 8, 9, 10, 13, 15, 21, 22, 25, 28, 29, 32, 33, 36, 38, 39, 40, 41, 47, 51, 52, 55, 56, 61, 63 ], [ 2, 3, 4, 8, 9, 16, 24, 28, 29, 30, 31, 32, 34, 35, 36, 39, 40, 41, 44, 48, 51, 53, 54, 56, 58, 60, 61, 64 ], [ 2, 3, 4, 8, 9, 16, 23, 24, 28, 29, 30, 31, 32, 34, 35, 36, 39, 40, 41, 43, 45, 48, 51, 53, 54, 56, 59, 61 ], [ 2, 3, 4, 8, 9, 15, 16, 24, 29, 30, 31, 32, 34, 35, 38, 39, 40, 41, 44, 48, 49, 53, 54, 58, 60, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 15, 16, 23, 24, 29, 30, 31, 32, 34, 35, 38, 39, 40, 41, 43, 45, 48, 49, 53, 54, 59, 61, 62 ], [ 2, 3, 4, 8, 9, 13, 16, 24, 28, 29, 30, 31, 32, 33, 36, 39, 40, 41, 44, 48, 51, 55, 56, 58, 60, 61, 63, 64 ], [ 2, 3, 4, 8, 9, 13, 16, 23, 24, 28, 29, 30, 31, 32, 33, 36, 39, 40, 41, 43, 45, 48, 51, 55, 56, 59, 61, 63 ], [ 2, 3, 4, 8, 9, 13, 15, 16, 24, 29, 30, 31, 32, 33, 38, 39, 40, 41, 44, 48, 49, 55, 58, 60, 61, 62, 63, 64 ], [ 2, 3, 4, 8, 9, 13, 15, 16, 23, 24, 29, 30, 31, 32, 33, 38, 39, 40, 41, 43, 45, 48, 49, 55, 59, 61, 62, 63 ], [ 2, 3, 4, 8, 9, 10, 13, 16, 25, 28, 29, 32, 33, 36, 39, 40, 41, 44, 47, 51, 52, 55, 56, 58, 60, 61, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 13, 16, 23, 25, 28, 29, 32, 33, 36, 39, 40, 41, 43, 45, 47, 51, 52, 55, 56, 59, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 13, 15, 16, 25, 29, 32, 33, 38, 39, 40, 41, 44, 47, 49, 52, 55, 58, 60, 61, 62, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 13, 15, 16, 23, 25, 29, 32, 33, 38, 39, 40, 41, 43, 45, 47, 49, 52, 55, 59, 61, 62, 63 ], [ 2, 3, 4, 7, 8, 9, 14, 21, 23, 26, 27, 30, 31, 32, 33, 39, 40, 41, 43, 44, 46, 53, 54, 58, 60, 61, 63, 64 ], [ 2, 3, 4, 7, 8, 9, 14, 21, 23, 26, 27, 28, 30, 31, 32, 33, 39, 40, 41, 43, 46, 49, 51, 53, 54, 61, 62, 63 ], [ 2, 3, 4, 7, 8, 9, 14, 15, 21, 23, 26, 27, 30, 31, 32, 33, 36, 38, 39, 40, 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