### 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 [64,169]. 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 [64,169]. # 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(64,169));' can be # used to create a list e of the elements of the group [64,169]. # In our list of (64,28,12) DSs in group [64,169], we have [1, # 2, 3, 4, 5, 7, 8, 9, 14, 18, 21, 23, 26, 28, 29, # 31, 32, 36, 38, 39, 40, 43, 44, 46, 51, 52, 61, 64]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[7], e[8], e[9], e[14], e[18], e[21], e[23], e[26], e[28], e[29], e[31], # e[32], e[36], e[38], e[39], e[40], e[43], e[44], e[46], e[51], e[52], e[61], e[64]] # where e is the list of the elements of the group [64,169] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,169));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 169] ### The number of inequivalent (64,28,12) DSs in group [64,169] is 796 ### The list of all inequivalent (64,28,12) DSs in group [64,169] is DS169:=[ [ 1, 2, 3, 4, 5, 7, 8, 9, 14, 18, 21, 23, 26, 28, 29, 31, 32, 36, 38, 39, 40, 43, 44, 46, 51, 52, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 14, 18, 21, 23, 25, 26, 29, 31, 32, 36, 38, 39, 40, 43, 44, 48, 49, 52, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 16, 17, 21, 23, 24, 25, 27, 28, 30, 38, 39, 41, 43, 52, 58, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 21, 24, 25, 28, 30, 36, 38, 40, 41, 43, 49, 50, 52, 57, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 21, 23, 24, 25, 28, 30, 36, 38, 40, 41, 44, 45, 49, 50, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 18, 21, 23, 24, 25, 27, 28, 30, 36, 38, 39, 40, 44, 45, 52, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 17, 18, 21, 23, 24, 25, 28, 30, 36, 38, 44, 45, 49, 50, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 18, 21, 23, 25, 26, 27, 28, 30, 39, 40, 43, 48, 52, 56, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 18, 21, 23, 24, 28, 29, 30, 39, 40, 43, 44, 46, 48, 51, 52, 56, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 18, 21, 23, 24, 27, 28, 30, 39, 40, 44, 45, 46, 48, 52, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 18, 19, 21, 23, 24, 28, 30, 41, 43, 44, 46, 48, 49, 50, 52, 56, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 17, 21, 24, 27, 28, 30, 39, 41, 43, 46, 48, 52, 56, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 17, 21, 23, 25, 26, 27, 28, 30, 39, 41, 43, 48, 52, 56, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 17, 21, 23, 24, 28, 29, 30, 39, 41, 43, 44, 46, 48, 51, 52, 56, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 17, 21, 23, 24, 27, 28, 30, 39, 41, 44, 45, 46, 48, 52, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 15, 17, 18, 21, 23, 24, 28, 30, 44, 45, 46, 48, 49, 50, 52, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 18, 21, 23, 26, 28, 29, 30, 31, 44, 46, 51, 56, 57, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 21, 24, 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20, 24, 25, 27, 29, 32, 34, 38, 40, 42, 43, 44, 45, 46, 51, 55, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 23, 24, 25, 29, 32, 38, 41, 45, 47, 49, 50, 53, 55, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 21, 25, 27, 32, 34, 38, 42, 45, 46, 50, 51, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 21, 24, 25, 32, 34, 38, 42, 45, 47, 49, 51, 58, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 21, 24, 25, 27, 32, 34, 38, 42, 44, 45, 47, 50, 51, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 21, 24, 27, 28, 30, 39, 42, 43, 45, 46, 50, 54, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 18, 20, 22, 31, 33, 36, 37, 39, 43, 44, 48, 51, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 18, 19, 21, 24, 27, 32, 38, 39, 42, 43, 44, 45, 55, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 19, 22, 25, 31, 33, 37, 42, 43, 45, 51, 56, 57, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 22, 23, 25, 28, 31, 36, 37, 40, 42, 43, 45, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 20, 22, 23, 31, 33, 36, 37, 40, 43, 45, 48, 51, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 21, 23, 28, 32, 41, 42, 43, 44, 46, 48, 49, 53, 55, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 21, 23, 24, 28, 32, 41, 42, 43, 47, 48, 49, 53, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 21, 23, 24, 27, 28, 32, 41, 42, 43, 44, 47, 48, 50, 53, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 20, 21, 24, 26, 28, 32, 41, 43, 46, 49, 55, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 20, 21, 23, 24, 26, 27, 29, 32, 41, 43, 44, 49, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 19, 20, 21, 23, 24, 32, 37, 38, 39, 41, 45, 50, 55, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 21, 26, 28, 32, 34, 42, 43, 46, 47, 49, 53, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 21, 23, 26, 27, 29, 32, 34, 42, 44, 47, 49, 53, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 21, 23, 26, 27, 28, 32, 34, 42, 45, 46, 47, 50, 53, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 17, 21, 22, 23, 26, 29, 34, 36, 37, 39, 41, 52, 55, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 17, 21, 22, 23, 26, 29, 33, 36, 37, 39, 41, 52, 54, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 21, 32, 39, 41, 42, 43, 44, 45, 47, 50, 55, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 20, 21, 32, 34, 36, 41, 43, 44, 45, 47, 50, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 20, 21, 24, 27, 32, 34, 39, 41, 43, 44, 45, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 19, 20, 23, 30, 35, 38, 40, 42, 43, 46, 49, 53, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 22, 26, 28, 29, 31, 35, 40, 42, 43, 44, 48, 55, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 21, 27, 32, 35, 36, 39, 40, 42, 43, 44, 47, 54, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 21, 23, 27, 32, 35, 36, 40, 41, 42, 44, 45, 47, 54, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 21, 22, 23, 26, 29, 34, 36, 38, 39, 40, 52, 55, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 21, 22, 23, 26, 29, 33, 36, 38, 39, 40, 52, 54, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 19, 25, 26, 30, 37, 38, 39, 44, 45, 46, 49, 51, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 22, 23, 26, 27, 31, 34, 35, 42, 43, 46, 48, 49, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 22, 23, 26, 27, 28, 31, 34, 35, 42, 46, 48, 51, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 20, 22, 25, 26, 29, 31, 35, 44, 49, 51, 55, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 22, 31, 36, 39, 41, 42, 43, 44, 48, 51, 54, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 19, 22, 23, 28, 31, 40, 42, 43, 44, 48, 53, 54, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 27, 29, 30, 36, 40, 41, 43, 45, 46, 47, 49, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 19, 27, 30, 36, 39, 43, 45, 46, 47, 50, 51, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 19, 25, 30, 36, 39, 44, 45, 47, 48, 49, 51, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 19, 20, 23, 30, 35, 37, 41, 42, 43, 46, 49, 53, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 22, 23, 31, 36, 40, 41, 42, 43, 45, 48, 51, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 19, 20, 22, 25, 31, 33, 39, 43, 45, 51, 53, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 19, 20, 22, 23, 28, 31, 36, 43, 44, 48, 54, 57, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 21, 23, 27, 32, 35, 38, 39, 40, 42, 44, 45, 47, 54, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 18, 21, 27, 32, 35, 38, 40, 41, 42, 43, 44, 47, 54, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 20, 24, 25, 27, 29, 32, 35, 38, 40, 42, 44, 45, 46, 51, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 20, 22, 25, 26, 27, 30, 33, 44, 45, 46, 50, 51, 56, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 22, 25, 26, 29, 31, 34, 37, 42, 44, 51, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 21, 24, 32, 33, 36, 37, 39, 42, 43, 50, 56, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 18, 21, 23, 24, 32, 33, 36, 37, 41, 42, 45, 50, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 21, 25, 26, 27, 28, 30, 39, 42, 43, 45, 50, 55, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 21, 24, 27, 32, 36, 38, 39, 42, 43, 44, 45, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 24, 27, 32, 36, 38, 41, 42, 43, 45, 54, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 20, 21, 32, 33, 36, 38, 41, 43, 45, 47, 50, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 21, 23, 24, 32, 33, 37, 38, 39, 42, 45, 50, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 18, 21, 24, 32, 33, 37, 38, 41, 42, 43, 50, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 21, 32, 36, 39, 40, 42, 43, 44, 45, 47, 50, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 18, 21, 32, 36, 40, 41, 42, 43, 45, 47, 50, 54, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 20, 30, 38, 40, 42, 43, 45, 46, 49, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 20, 22, 25, 26, 27, 31, 40, 43, 45, 46, 49, 55, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 20, 22, 25, 26, 27, 28, 31, 40, 45, 46, 51, 55, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 20, 22, 25, 31, 37, 38, 39, 40, 45, 51, 55, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 19, 20, 30, 37, 41, 42, 43, 45, 46, 49, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 29, 30, 31, 34, 37, 39, 41, 43, 45, 46, 52, 54, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 22, 24, 25, 27, 36, 42, 43, 45, 47, 49, 54, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 20, 25, 27, 42, 44, 45, 46, 47, 49, 51, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 20, 25, 27, 42, 43, 45, 46, 47, 49, 51, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 20, 24, 28, 42, 44, 45, 46, 48, 49, 50, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 20, 24, 28, 42, 43, 45, 46, 48, 49, 50, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 26, 29, 30, 34, 36, 37, 39, 41, 45, 52, 55, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 26, 29, 30, 33, 36, 37, 39, 41, 45, 52, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 26, 29, 30, 34, 36, 38, 39, 40, 45, 52, 55, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 26, 29, 30, 33, 36, 38, 39, 40, 45, 52, 54, 58, 63 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 445 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS169[2], DS169[5], DS169[8], DS169[9], DS169[11], DS169[13], DS169[14], DS169[19], DS169[27], DS169[35], DS169[41], DS169[42], DS169[43], DS169[44], DS169[45], DS169[47], DS169[52], DS169[53], DS169[54], DS169[55], DS169[56], DS169[57], DS169[58], DS169[61], DS169[62], DS169[63], DS169[64], DS169[65], DS169[67], DS169[68], DS169[71], DS169[75], DS169[81], DS169[82], DS169[83], DS169[84], DS169[86], DS169[87], DS169[88], DS169[90], DS169[91], DS169[94], DS169[96], DS169[97], DS169[100], DS169[101], DS169[102], DS169[106], DS169[111], DS169[114], DS169[119], DS169[120], DS169[121], DS169[122], DS169[127], DS169[131], DS169[132], DS169[133], DS169[136], DS169[138], DS169[139], DS169[143], DS169[146], DS169[147], DS169[150], DS169[156], DS169[157], DS169[159], DS169[162], DS169[163], DS169[164], DS169[168], DS169[177], DS169[185], DS169[186], DS169[191], DS169[193], DS169[194], DS169[195], DS169[196], DS169[197], DS169[198], DS169[199], DS169[202], DS169[203], DS169[204], DS169[205], DS169[206], DS169[207], DS169[209], DS169[210], DS169[213], DS169[215], DS169[216], DS169[220], DS169[225], DS169[229], DS169[230], DS169[232], DS169[234], DS169[237], DS169[238], DS169[239], DS169[240], DS169[241], DS169[242], DS169[245], DS169[246], DS169[247], DS169[248], DS169[250], DS169[251], DS169[252], DS169[253], DS169[257], DS169[258], DS169[260], DS169[262], DS169[263], DS169[264], DS169[269], DS169[270], DS169[272], DS169[273], DS169[280], DS169[282], DS169[283], DS169[287], DS169[289], DS169[290], DS169[295], DS169[297], DS169[298], DS169[299], DS169[301], DS169[302], DS169[303], DS169[304], DS169[305], DS169[308], DS169[309], DS169[310], DS169[315], DS169[317], DS169[318], DS169[320], DS169[321], DS169[322], DS169[323], DS169[325], DS169[326], DS169[328], DS169[329], DS169[330], DS169[331], DS169[332], DS169[333], DS169[334], DS169[335], DS169[336], DS169[337], DS169[339], DS169[340], DS169[341], DS169[342], DS169[345], DS169[349], DS169[350], DS169[356], DS169[358], DS169[359], DS169[362], DS169[363], DS169[367], DS169[368], DS169[370], DS169[371], DS169[372], DS169[373], DS169[376], DS169[377], DS169[380], DS169[381], DS169[382], DS169[383], DS169[384], DS169[386], DS169[388], DS169[389], DS169[391], DS169[392], DS169[394], DS169[395], DS169[396], DS169[398], DS169[399], DS169[403], DS169[404], DS169[405], DS169[410], DS169[411], DS169[414], DS169[415], DS169[416], DS169[417], DS169[419], DS169[421], DS169[424], DS169[425], DS169[427], DS169[429], DS169[433], DS169[435], DS169[436], DS169[437], DS169[438], DS169[439], DS169[444], DS169[445], DS169[448], DS169[451], DS169[460], DS169[464], DS169[466], DS169[473], DS169[474], DS169[475], DS169[476], DS169[477], DS169[478], DS169[479], DS169[480], DS169[481], DS169[482], DS169[483], DS169[484], DS169[485], DS169[486], DS169[487], DS169[488], DS169[491], DS169[493], DS169[497], DS169[498], DS169[499], DS169[502], DS169[503], DS169[509], DS169[511], DS169[514], DS169[517], DS169[520], DS169[525], DS169[526], DS169[529], DS169[530], DS169[531], DS169[532], DS169[535], DS169[536], DS169[539], DS169[540], DS169[541], DS169[542], DS169[543], DS169[544], DS169[549], DS169[550], DS169[551], DS169[552], DS169[553], DS169[554], DS169[555], DS169[556], DS169[558], DS169[560], DS169[561], DS169[563], DS169[564], DS169[565], DS169[568], DS169[569], DS169[570], DS169[571], DS169[572], DS169[573], DS169[575], DS169[584], DS169[592], DS169[595], DS169[596], DS169[599], DS169[600], DS169[602], DS169[603], DS169[604], DS169[605], DS169[606], DS169[607], DS169[608], DS169[609], DS169[610], DS169[611], DS169[612], DS169[613], DS169[614], DS169[615], DS169[616], DS169[617], DS169[618], DS169[619], DS169[622], DS169[623], DS169[624], DS169[625], DS169[626], DS169[627], DS169[628], DS169[629], DS169[631], DS169[633], DS169[635], DS169[638], DS169[641], DS169[645], DS169[646], DS169[648], DS169[649], DS169[650], DS169[655], DS169[656], DS169[657], DS169[658], DS169[659], DS169[662], DS169[663], DS169[664], DS169[665], DS169[666], DS169[667], DS169[668], DS169[669], DS169[670], DS169[671], DS169[672], DS169[673], DS169[674], DS169[675], DS169[676], DS169[677], DS169[678], DS169[679], DS169[680], DS169[681], DS169[682], DS169[683], DS169[684], DS169[685], DS169[686], DS169[691], DS169[692], DS169[696], DS169[697], DS169[699], DS169[702], DS169[704], DS169[705], DS169[708], DS169[710], DS169[711], DS169[712], DS169[713], DS169[714], DS169[715], DS169[716], DS169[717], DS169[718], DS169[719], DS169[720], DS169[721], DS169[722], DS169[723], DS169[724], DS169[725], DS169[726], DS169[727], DS169[728], DS169[729], DS169[730], DS169[731], DS169[732], DS169[733], DS169[734], DS169[735], DS169[736], DS169[737], DS169[738], DS169[739], DS169[740], DS169[741], DS169[742], DS169[745], DS169[746], DS169[747], DS169[748], DS169[749], DS169[750], DS169[751], DS169[754], DS169[755], DS169[756], DS169[757], DS169[758], DS169[759], DS169[760], DS169[761], DS169[762], DS169[763], DS169[764], DS169[765], DS169[766], DS169[767], DS169[768], DS169[769], DS169[770], DS169[771], DS169[772], DS169[773], DS169[774], DS169[775], DS169[776], DS169[777], DS169[778], DS169[779], DS169[780], DS169[781], DS169[783], DS169[784], DS169[785], DS169[787], DS169[788], DS169[789], DS169[790], DS169[791], DS169[793]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,169]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,169] is 96 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,169] is RDS169:=[ [ 3, 4, 5, 8, 9, 15, 20, 21, 24, 25, 27, 33, 34, 36, 37, 40, 41, 42, 44, 49, 51, 54, 55, 57, 58, 60, 61, 64 ], [ 3, 4, 5, 8, 9, 15, 20, 21, 23, 24, 25, 28, 33, 34, 36, 37, 40, 41, 42, 43, 45, 49, 50, 54, 55, 57, 59, 61 ], [ 3, 4, 5, 8, 9, 15, 20, 21, 23, 24, 25, 27, 33, 34, 36, 37, 40, 41, 42, 43, 45, 49, 51, 54, 55, 57, 59, 61 ], [ 3, 4, 5, 8, 9, 13, 15, 20, 21, 24, 25, 27, 35, 36, 37, 40, 41, 42, 44, 49, 51, 53, 57, 58, 60, 61, 63, 64 ], [ 3, 4, 5, 8, 9, 13, 15, 20, 21, 23, 24, 25, 28, 35, 36, 37, 40, 41, 42, 43, 45, 49, 50, 53, 57, 59, 61, 63 ], [ 3, 4, 5, 8, 9, 13, 15, 20, 21, 23, 24, 25, 27, 35, 36, 37, 40, 41, 42, 43, 45, 49, 51, 53, 57, 59, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 24, 25, 27, 30, 34, 38, 42, 43, 44, 49, 51, 54, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 24, 25, 27, 30, 33, 38, 42, 43, 44, 49, 51, 55, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 23, 24, 25, 27, 30, 34, 38, 42, 45, 49, 51, 54, 58, 61, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 23, 24, 25, 27, 30, 33, 38, 42, 45, 49, 51, 55, 58, 61, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 15, 16, 21, 22, 24, 25, 27, 30, 34, 38, 44, 49, 51, 54, 58, 60, 61, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 15, 16, 21, 22, 24, 25, 27, 30, 33, 38, 44, 49, 51, 55, 58, 60, 61, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 15, 16, 21, 22, 23, 24, 25, 27, 30, 34, 38, 43, 45, 49, 51, 54, 59, 61, 63 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 15, 16, 21, 22, 23, 24, 25, 27, 30, 33, 38, 43, 45, 49, 51, 55, 59, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 12, 15, 23, 28, 31, 33, 34, 36, 37, 40, 41, 44, 45, 47, 48, 49, 50, 54, 55, 57, 60, 61 ], [ 2, 3, 4, 8, 9, 10, 12, 15, 23, 24, 25, 28, 31, 33, 34, 36, 37, 40, 41, 44, 45, 49, 50, 54, 55, 57, 60, 61 ], [ 2, 3, 4, 8, 9, 10, 12, 15, 23, 24, 25, 27, 31, 33, 34, 36, 37, 40, 41, 44, 45, 49, 51, 54, 55, 57, 60, 61 ], [ 2, 3, 4, 8, 9, 10, 12, 13, 15, 23, 28, 31, 35, 36, 37, 40, 41, 44, 45, 47, 48, 49, 50, 53, 57, 60, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 12, 13, 15, 23, 24, 25, 28, 31, 35, 36, 37, 40, 41, 44, 45, 49, 50, 53, 57, 60, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 12, 13, 15, 23, 24, 25, 27, 31, 35, 36, 37, 40, 41, 44, 45, 49, 51, 53, 57, 60, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 11, 15, 16, 17, 19, 24, 25, 27, 30, 34, 35, 38, 40, 43, 44, 49, 51, 53, 54, 59, 60, 61 ], [ 2, 3, 4, 8, 9, 10, 11, 15, 16, 17, 19, 23, 24, 25, 27, 30, 34, 35, 38, 40, 45, 49, 51, 53, 54, 58, 61, 64 ], [ 2, 3, 4, 8, 9, 10, 11, 13, 15, 16, 17, 19, 24, 25, 27, 30, 34, 38, 40, 43, 44, 49, 51, 54, 59, 60, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 11, 13, 15, 16, 17, 19, 24, 25, 27, 30, 33, 38, 40, 43, 44, 49, 51, 55, 59, 60, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 11, 13, 15, 16, 17, 19, 23, 24, 25, 27, 30, 34, 38, 40, 45, 49, 51, 54, 58, 61, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 11, 13, 15, 16, 17, 19, 23, 24, 25, 27, 30, 33, 38, 40, 45, 49, 51, 55, 58, 61, 63, 64 ], [ 2, 3, 4, 5, 9, 10, 11, 15, 20, 21, 23, 27, 33, 34, 36, 37, 40, 41, 42, 43, 45, 49, 51, 52, 54, 55, 57, 59 ], [ 2, 3, 4, 5, 9, 10, 11, 13, 15, 20, 21, 23, 27, 35, 36, 37, 40, 41, 42, 43, 45, 49, 51, 52, 53, 57, 59, 63 ], [ 2, 3, 4, 5, 8, 10, 15, 20, 21, 23, 24, 25, 30, 32, 33, 34, 36, 37, 40, 41, 42, 43, 45, 54, 55, 57, 59, 61 ], [ 2, 3, 4, 5, 8, 10, 13, 15, 20, 21, 23, 24, 25, 30, 32, 35, 36, 37, 40, 41, 42, 43, 45, 53, 57, 59, 61, 63 ], [ 2, 3, 4, 5, 8, 9, 15, 20, 21, 23, 26, 27, 31, 32, 36, 37, 40, 41, 42, 43, 45, 46, 49, 51, 52, 57, 59, 61 ], [ 2, 3, 4, 5, 8, 9, 12, 15, 20, 21, 28, 30, 36, 37, 40, 41, 42, 44, 47, 48, 49, 50, 52, 57, 58, 60, 61, 64 ], [ 2, 3, 4, 5, 8, 9, 12, 15, 20, 21, 24, 25, 27, 30, 36, 37, 40, 41, 42, 44, 49, 51, 52, 57, 58, 60, 61, 64 ], [ 2, 3, 4, 5, 8, 9, 12, 15, 20, 21, 23, 28, 30, 36, 37, 40, 41, 42, 43, 45, 47, 48, 49, 50, 52, 57, 59, 61 ], [ 2, 3, 4, 5, 8, 9, 12, 15, 20, 21, 23, 27, 30, 36, 37, 40, 41, 42, 43, 45, 47, 48, 49, 51, 52, 57, 59, 61 ], [ 2, 3, 4, 5, 8, 9, 12, 15, 20, 21, 23, 24, 25, 28, 30, 36, 37, 40, 41, 42, 43, 45, 49, 50, 52, 57, 59, 61 ], [ 2, 3, 4, 5, 8, 9, 12, 15, 20, 21, 23, 24, 25, 27, 30, 36, 37, 40, 41, 42, 43, 45, 49, 51, 52, 57, 59, 61 ], [ 2, 3, 4, 5, 8, 9, 11, 15, 20, 21, 23, 24, 25, 29, 30, 31, 36, 37, 40, 41, 42, 43, 45, 49, 57, 59, 61, 62 ], [ 2, 3, 4, 5, 8, 9, 10, 15, 20, 21, 23, 24, 25, 29, 30, 32, 36, 37, 40, 41, 42, 43, 45, 49, 57, 59, 61, 62 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 24, 25, 28, 31, 33, 34, 36, 37, 40, 41, 42, 49, 50, 54, 55, 57, 61 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 24, 25, 27, 31, 33, 34, 36, 37, 40, 41, 42, 49, 51, 54, 55, 57, 61 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 28, 31, 36, 37, 40, 41, 42, 45, 47, 48, 49, 50, 57, 58, 61, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 27, 31, 36, 37, 40, 41, 42, 45, 47, 48, 49, 51, 57, 58, 61, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 24, 25, 28, 31, 36, 37, 40, 41, 42, 45, 49, 50, 57, 58, 61, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 24, 25, 27, 31, 36, 37, 40, 41, 42, 45, 49, 51, 57, 58, 61, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 13, 15, 20, 21, 24, 25, 28, 31, 35, 36, 37, 40, 41, 42, 49, 50, 53, 57, 61, 63 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 13, 15, 20, 21, 24, 25, 27, 31, 35, 36, 37, 40, 41, 42, 49, 51, 53, 57, 61, 63 ], [ 2, 3, 4, 5, 8, 9, 10, 11, 15, 20, 21, 23, 26, 27, 36, 37, 40, 41, 42, 43, 45, 46, 49, 51, 52, 57, 59, 61 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 21, 22, 23, 28, 31, 36, 37, 40, 41, 44, 45, 47, 48, 49, 50, 57, 60, 61 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 21, 22, 23, 24, 25, 28, 31, 36, 37, 40, 41, 44, 45, 49, 50, 57, 60, 61 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 21, 22, 23, 24, 25, 27, 31, 36, 37, 40, 41, 44, 45, 49, 51, 57, 60, 61 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 15, 16, 17, 19, 21, 22, 24, 25, 27, 30, 34, 35, 38, 40, 49, 51, 53, 54, 61 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 24, 25, 27, 30, 34, 38, 40, 49, 51, 54, 61, 63 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 24, 25, 27, 30, 33, 38, 40, 49, 51, 55, 61, 63 ], [ 1, 3, 4, 5, 7, 8, 9, 15, 21, 23, 28, 33, 34, 36, 37, 40, 41, 44, 45, 47, 48, 49, 50, 54, 55, 57, 60, 61 ], [ 1, 3, 4, 5, 7, 8, 9, 15, 21, 23, 24, 25, 28, 33, 34, 36, 37, 40, 41, 44, 45, 49, 50, 54, 55, 57, 60, 61 ], [ 1, 3, 4, 5, 7, 8, 9, 15, 21, 23, 24, 25, 27, 33, 34, 36, 37, 40, 41, 44, 45, 49, 51, 54, 55, 57, 60, 61 ], [ 1, 3, 4, 5, 7, 8, 9, 13, 15, 21, 23, 28, 35, 36, 37, 40, 41, 44, 45, 47, 48, 49, 50, 53, 57, 60, 61, 63 ], [ 1, 3, 4, 5, 7, 8, 9, 13, 15, 21, 23, 24, 25, 28, 35, 36, 37, 40, 41, 44, 45, 49, 50, 53, 57, 60, 61, 63 ], [ 1, 3, 4, 5, 7, 8, 9, 13, 15, 21, 23, 24, 25, 27, 35, 36, 37, 40, 41, 44, 45, 49, 51, 53, 57, 60, 61, 63 ], [ 1, 2, 3, 7, 8, 9, 10, 11, 13, 15, 16, 20, 24, 25, 27, 30, 34, 38, 42, 44, 49, 51, 54, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 7, 8, 9, 10, 11, 13, 15, 16, 20, 24, 25, 27, 30, 33, 38, 42, 44, 49, 51, 55, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 7, 8, 9, 10, 11, 13, 15, 16, 20, 23, 24, 25, 27, 30, 34, 38, 42, 43, 45, 49, 51, 54, 59, 61, 63 ], [ 1, 2, 3, 7, 8, 9, 10, 11, 13, 15, 16, 20, 23, 24, 25, 27, 30, 33, 38, 42, 43, 45, 49, 51, 55, 59, 61, 63 ], [ 1, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 21, 24, 25, 27, 30, 34, 38, 43, 44, 49, 51, 54, 59, 60, 61, 63 ], [ 1, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 21, 24, 25, 27, 30, 33, 38, 43, 44, 49, 51, 55, 59, 60, 61, 63 ], [ 1, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 21, 23, 24, 25, 27, 30, 34, 38, 45, 49, 51, 54, 58, 61, 63, 64 ], [ 1, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 21, 23, 24, 25, 27, 30, 33, 38, 45, 49, 51, 55, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 12, 15, 20, 23, 28, 31, 36, 37, 40, 41, 42, 44, 45, 47, 48, 49, 50, 57, 60, 61 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 12, 15, 20, 23, 24, 25, 28, 31, 36, 37, 40, 41, 42, 44, 45, 49, 50, 57, 60, 61 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 12, 15, 20, 23, 24, 25, 27, 31, 36, 37, 40, 41, 42, 44, 45, 49, 51, 57, 60, 61 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 15, 16, 17, 19, 20, 24, 25, 27, 30, 34, 35, 38, 40, 42, 49, 51, 53, 54, 61 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 20, 24, 25, 27, 30, 34, 38, 40, 42, 49, 51, 54, 61, 63 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 20, 24, 25, 27, 30, 33, 38, 40, 42, 49, 51, 55, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 15, 21, 23, 27, 33, 34, 36, 37, 40, 41, 44, 45, 49, 51, 52, 54, 55, 57, 60 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 21, 23, 27, 35, 36, 37, 40, 41, 44, 45, 49, 51, 52, 53, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 15, 21, 23, 24, 25, 30, 32, 33, 34, 36, 37, 40, 41, 44, 45, 54, 55, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 21, 23, 24, 25, 30, 32, 35, 36, 37, 40, 41, 44, 45, 53, 57, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 15, 21, 23, 26, 27, 31, 32, 36, 37, 40, 41, 44, 45, 46, 49, 51, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 21, 28, 30, 36, 37, 40, 41, 43, 47, 48, 49, 50, 52, 57, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 21, 24, 25, 27, 30, 36, 37, 40, 41, 43, 49, 51, 52, 57, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 21, 23, 28, 30, 36, 37, 40, 41, 44, 45, 47, 48, 49, 50, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 21, 23, 27, 30, 36, 37, 40, 41, 44, 45, 47, 48, 49, 51, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 21, 23, 24, 25, 28, 30, 36, 37, 40, 41, 44, 45, 49, 50, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 21, 23, 24, 25, 27, 30, 36, 37, 40, 41, 44, 45, 49, 51, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 21, 23, 24, 25, 29, 30, 31, 36, 37, 40, 41, 44, 45, 49, 57, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 24, 25, 28, 32, 33, 34, 36, 37, 40, 41, 49, 50, 54, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 24, 25, 27, 32, 33, 34, 36, 37, 40, 41, 49, 51, 54, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 23, 28, 32, 36, 37, 40, 41, 45, 47, 48, 49, 50, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 23, 27, 32, 36, 37, 40, 41, 45, 47, 48, 49, 51, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 23, 24, 25, 28, 32, 36, 37, 40, 41, 45, 49, 50, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 23, 24, 25, 27, 32, 36, 37, 40, 41, 45, 49, 51, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 21, 24, 25, 28, 32, 35, 36, 37, 40, 41, 49, 50, 53, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 21, 24, 25, 27, 32, 35, 36, 37, 40, 41, 49, 51, 53, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 15, 21, 23, 24, 25, 29, 30, 32, 36, 37, 40, 41, 44, 45, 49, 57, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 21, 23, 26, 27, 36, 37, 40, 41, 44, 45, 46, 49, 51, 52, 57, 60, 61 ] ]; ########################### ########################### ###########################