### 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 [64,121]. 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 [64,121].
    
    
# 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(64,121));' can be 
# used to create a list e of the elements of the group [64,121].
# In our list of (64,28,12) DSs in group [64,121], we have [1, 
# 2, 3, 4, 5, 9, 10, 12, 13, 15, 19, 22, 23, 28, 29, 
# 31, 33, 37, 39, 42, 43, 44, 51, 55, 56, 57, 58, 63].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[9], e[10], e[12], e[13], e[15], e[19], e[22], e[23], e[28], e[29], e[31], 
# e[33], e[37], e[39], e[42], e[43], e[44], e[51], e[55], e[56], e[57], e[58], e[63]]
# where e is the list of the elements of the group [64,121] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,121));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 121]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,121] is 1808
### The list of all inequivalent (64,28,12) DSs in group [64,121] is 
  
  
DS121:=[ [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 15, 19, 22, 23, 28, 29, 31, 33, 37, 39, 42, 43, 44, 51, 55, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 14, 15, 19, 22, 31, 34, 35, 36, 39, 42, 45, 49, 50, 51, 55, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 14, 15, 19, 22, 31, 34, 35, 36, 39, 42, 43, 45, 49, 50, 51, 55, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 14, 15, 19, 22, 23, 31, 34, 35, 36, 39, 42, 44, 49, 50, 51, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 14, 15, 19, 22, 23, 31, 34, 35, 36, 39, 42, 43, 44, 49, 50, 51, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 14, 15, 19, 22, 23, 28, 29, 31, 33, 36, 39, 42, 43, 44, 51, 55, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 18, 22, 23, 26, 31, 33, 38, 40, 42, 43, 45, 46, 52, 55, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 18, 22, 23, 26, 31, 33, 38, 39, 42, 43, 45, 46, 52, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 16, 18, 22, 23, 25, 26, 30, 33, 36, 40, 42, 43, 45, 48, 55, 56, 57, 59, 63 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 16, 17, 18, 22, 23, 25, 26, 30, 33, 36, 39, 42, 43, 45, 48, 55, 56, 59, 63 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 15, 16, 18, 22, 23, 26, 30, 33, 38, 40, 42, 43, 45, 46, 55, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 15, 16, 17, 18, 22, 23, 26, 30, 33, 38, 39, 42, 43, 45, 46, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 24, 25, 27, 29, 30, 31, 32, 34, 38, 39, 42, 46, 50, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 24, 25, 27, 29, 30, 31, 32, 33, 34, 38, 39, 42, 46, 50, 53, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 15, 17, 19, 22, 23, 25, 26, 30, 36, 40, 42, 44, 48, 49, 50, 51, 52, 59, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 15, 17, 19, 22, 23, 25, 26, 30, 36, 40, 42, 43, 44, 48, 49, 50, 51, 52, 58 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 15, 17, 19, 22, 23, 25, 26, 27, 30, 36, 40, 42, 44, 48, 51, 52, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 15, 17, 19, 22, 23, 25, 26, 27, 30, 36, 40, 42, 43, 44, 48, 51, 52, 58, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 15, 16, 17, 22, 24, 25, 27, 29, 30, 34, 38, 41, 42, 46, 50, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 15, 16, 17, 22, 24, 25, 27, 29, 30, 33, 34, 38, 41, 42, 46, 50, 52, 53, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 15, 17, 19, 22, 23, 26, 27, 32, 37, 40, 42, 44, 46, 51, 56, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 15, 17, 19, 22, 23, 26, 27, 32, 37, 40, 42, 43, 44, 46, 51, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 17, 19, 22, 23, 26, 27, 32, 36, 40, 42, 44, 46, 51, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 17, 19, 22, 23, 26, 27, 32, 36, 40, 42, 43, 44, 46, 51, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 16, 17, 22, 24, 25, 27, 29, 32, 34, 36, 41, 42, 46, 50, 54, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 16, 17, 22, 24, 25, 27, 29, 32, 33, 34, 36, 41, 42, 46, 50, 53, 56, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 25, 27, 29, 32, 34, 36, 41, 42, 47, 50, 52, 54, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 25, 27, 29, 32, 33, 34, 36, 41, 42, 47, 50, 52, 53, 56, 61 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 24, 25, 27, 29, 32, 34, 36, 41, 42, 46, 50, 52, 54, 56, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 24, 25, 27, 29, 32, 33, 34, 36, 41, 42, 46, 50, 52, 53, 56 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 15, 16, 19, 22, 24, 25, 27, 29, 32, 34, 38, 39, 42, 46, 50, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 15, 16, 19, 22, 24, 25, 27, 29, 32, 33, 34, 38, 39, 42, 46, 50, 52, 53, 57 ], [ 1, 2, 3, 4, 5, 7, 9, 12, 13, 14, 15, 17, 21, 23, 30, 34, 35, 36, 41, 44, 49, 50, 51, 52, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 12, 13, 14, 15, 17, 21, 23, 30, 34, 35, 36, 41, 43, 44, 49, 50, 51, 52, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 12, 13, 14, 15, 17, 21, 23, 27, 30, 34, 35, 36, 41, 44, 51, 52, 55, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 12, 13, 14, 15, 17, 21, 23, 27, 30, 34, 35, 36, 41, 43, 44, 51, 52, 55, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 15, 17, 21, 23, 27, 32, 35, 37, 41, 44, 51, 53, 56, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 15, 17, 21, 23, 27, 32, 35, 37, 41, 43, 44, 51, 53, 56, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 17, 21, 23, 27, 32, 35, 36, 41, 44, 51, 53, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 17, 21, 23, 27, 32, 35, 36, 41, 43, 44, 51, 53, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 14, 15, 19, 21, 23, 27, 32, 33, 36, 39, 43, 44, 51, 52, 53, 54, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 14, 15, 17, 21, 29, 32, 33, 36, 41, 45, 49, 52, 53, 54, 57, 59, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 14, 15, 17, 21, 29, 32, 33, 36, 41, 43, 45, 49, 52, 53, 54, 57, 58, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 14, 15, 17, 21, 23, 29, 32, 33, 36, 41, 44, 49, 52, 53, 54, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 14, 15, 17, 21, 23, 29, 32, 33, 36, 41, 43, 44, 49, 52, 53, 54, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 15, 17, 21, 23, 28, 29, 32, 35, 37, 41, 44, 51, 52, 53, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 15, 17, 21, 23, 28, 29, 32, 35, 37, 41, 43, 44, 51, 52, 53, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 19, 21, 23, 27, 32, 34, 35, 36, 39, 43, 44, 51, 52, 55, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 18, 19, 21, 23, 27, 32, 35, 36, 41, 44, 51, 52, 53, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 18, 19, 21, 23, 27, 32, 35, 36, 41, 43, 44, 51, 52, 53, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 17, 21, 29, 32, 34, 35, 36, 41, 45, 49, 52, 55, 57, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 17, 21, 29, 32, 34, 35, 36, 41, 43, 45, 49, 52, 55, 57, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 17, 21, 23, 29, 32, 34, 35, 36, 41, 44, 49, 52, 55, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 17, 21, 23, 29, 32, 34, 35, 36, 41, 43, 44, 49, 52, 55, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 17, 21, 23, 28, 29, 32, 35, 36, 41, 44, 51, 52, 53, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 15, 17, 21, 23, 28, 29, 32, 35, 36, 41, 43, 44, 51, 52, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 18, 21, 23, 26, 31, 33, 38, 39, 46, 52, 55, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 18, 21, 23, 26, 31, 33, 38, 39, 43, 46, 52, 55, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 18, 21, 23, 24, 31, 38, 39, 45, 48, 52, 53, 54, 55, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 18, 21, 23, 24, 31, 35, 38, 39, 43, 48, 52, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 18, 21, 23, 24, 31, 33, 38, 39, 45, 48, 52, 55, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 16, 17, 18, 21, 23, 24, 30, 33, 36, 39, 43, 48, 53, 54, 56, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 17, 18, 21, 23, 30, 33, 38, 39, 45, 46, 47, 48, 53, 54, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 17, 18, 21, 23, 26, 30, 33, 38, 39, 46, 53, 54, 56, 58, 59, 60, 61, 63 ], [ 1, 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61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 27, 30, 31, 33, 34, 38, 39, 40, 46, 55, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 20, 21, 27, 28, 29, 33, 38, 45, 46, 53, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 25, 30, 31, 33, 36, 41, 50, 53, 55, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 21, 27, 35, 37, 38, 40, 42, 46, 49, 50, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 27, 30, 31, 37, 38, 40, 41, 46, 53, 54, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 19, 30, 31, 35, 36, 37, 41, 48, 50, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 25, 29, 37, 38, 39, 40, 46, 49, 51, 54, 55, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 25, 33, 37, 38, 39, 41, 46, 49, 50, 53, 55, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 30, 33, 38, 39, 41, 43, 49, 52, 54, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 30, 34, 38, 39, 40, 43, 49, 52, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 31, 35, 38, 39, 40, 43, 50, 52, 55, 60, 61, 63 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 904
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS121[1], DS121[6], DS121[7], DS121[9], DS121[10], DS121[11], DS121[14], DS121[23], DS121[26], DS121[29], DS121[30], DS121[33], DS121[36], DS121[37], DS121[38], DS121[41], DS121[46], DS121[52], DS121[55], DS121[57], DS121[58], DS121[63], DS121[64], DS121[65], DS121[73], DS121[75], DS121[76], DS121[79], DS121[82], DS121[83], DS121[87], DS121[91], DS121[93], DS121[94], DS121[95], DS121[104], DS121[105], DS121[106], DS121[107], DS121[110], DS121[111], DS121[114], DS121[116], DS121[117], DS121[118], DS121[121], DS121[122], DS121[123], DS121[124], DS121[125], DS121[126], DS121[127], DS121[132], DS121[133], DS121[136], DS121[137], DS121[142], DS121[146], DS121[147], DS121[149], DS121[150], DS121[151], DS121[154], DS121[155], DS121[161], DS121[162], DS121[163], DS121[164], DS121[170], DS121[172], DS121[174], DS121[176], DS121[178], DS121[179], DS121[182], DS121[183], DS121[187], DS121[188], DS121[194], DS121[195], DS121[197], DS121[200], DS121[201], DS121[202], DS121[203], DS121[208], DS121[209], DS121[215], DS121[226], DS121[233], DS121[239], DS121[243], DS121[247], DS121[253], DS121[254], DS121[255], DS121[257], DS121[258], DS121[261], DS121[262], DS121[268], DS121[272], DS121[278], DS121[280], DS121[281], DS121[290], DS121[292], DS121[294], DS121[295], DS121[298], DS121[305], DS121[307], DS121[309], DS121[310], DS121[312], DS121[325], DS121[336], DS121[338], DS121[347], DS121[348], DS121[359], DS121[369], DS121[372], DS121[374], DS121[385], DS121[386], DS121[393], DS121[405], DS121[427], DS121[428], DS121[434], DS121[435], DS121[436], DS121[441], DS121[442], DS121[444], DS121[445], DS121[450], DS121[451], DS121[452], DS121[453], DS121[461], DS121[463], DS121[467], DS121[468], DS121[471], DS121[473], DS121[481], DS121[485], DS121[494], DS121[495], DS121[499], DS121[503], DS121[504], DS121[505], DS121[507], DS121[508], DS121[516], DS121[517], DS121[525], DS121[526], DS121[528], DS121[531], DS121[532], DS121[533], DS121[537], DS121[539], DS121[541], DS121[543], DS121[544], DS121[545], DS121[547], DS121[549], DS121[551], DS121[552], DS121[557], DS121[558], DS121[561], DS121[568], DS121[573], DS121[574], DS121[575], DS121[578], DS121[586], DS121[587], DS121[592], DS121[594], DS121[595], DS121[596], DS121[597], DS121[598], DS121[599], DS121[601], DS121[605], DS121[607], DS121[608], DS121[609], DS121[610], DS121[614], DS121[616], DS121[619], DS121[622], DS121[623], DS121[624], DS121[625], DS121[626], DS121[628], DS121[631], DS121[634], DS121[636], DS121[637], DS121[642], DS121[644], DS121[645], DS121[646], DS121[647], DS121[648], DS121[650], DS121[655], DS121[656], DS121[657], DS121[667], DS121[671], DS121[672], DS121[676], DS121[680], DS121[681], DS121[682], DS121[683], DS121[694], DS121[695], DS121[696], DS121[701], DS121[702], DS121[705], DS121[710], DS121[713], DS121[722], DS121[723], DS121[728], DS121[731], DS121[733], DS121[745], DS121[748], DS121[749], DS121[750], DS121[754], DS121[757], DS121[760], DS121[761], DS121[762], DS121[763], DS121[764], DS121[765], DS121[766], DS121[767], DS121[779], DS121[781], DS121[782], DS121[783], DS121[784], DS121[785], DS121[787], DS121[788], DS121[789], DS121[790], DS121[791], DS121[801], DS121[808], DS121[816], DS121[820], DS121[822], DS121[823], DS121[824], DS121[825], DS121[837], DS121[842], DS121[843], DS121[856], DS121[857], DS121[862], DS121[863], DS121[864], DS121[865], DS121[869], DS121[873], DS121[874], DS121[877], DS121[886], DS121[892], DS121[895], DS121[896], DS121[899], DS121[902], DS121[903], DS121[904], DS121[905], DS121[906], DS121[907], DS121[908], DS121[909], DS121[911], DS121[912], DS121[913], DS121[915], DS121[916], DS121[919], DS121[922], DS121[923], DS121[924], DS121[925], DS121[926], DS121[929], DS121[930], DS121[931], DS121[932], DS121[933], DS121[934], DS121[936], DS121[940], DS121[941], DS121[942], DS121[944], DS121[947], DS121[948], DS121[949], DS121[950], DS121[958], DS121[959], DS121[966], DS121[967], DS121[971], DS121[972], DS121[973], DS121[974], DS121[975], DS121[976], DS121[977], DS121[978], DS121[979], DS121[980], DS121[982], DS121[983], DS121[986], DS121[988], DS121[989], DS121[990], DS121[991], DS121[992], DS121[993], DS121[994], DS121[997], DS121[998], DS121[1001], DS121[1002], DS121[1003], DS121[1004], DS121[1008], DS121[1012], DS121[1022], DS121[1024], DS121[1025], DS121[1028], DS121[1030], DS121[1032], DS121[1039], DS121[1040], DS121[1043], DS121[1047], DS121[1049], DS121[1051], DS121[1062], DS121[1063], DS121[1064], DS121[1069], DS121[1070], DS121[1075], DS121[1076], DS121[1079], DS121[1087], DS121[1088], DS121[1090], DS121[1093], DS121[1094], DS121[1096], DS121[1097], DS121[1098], DS121[1101], DS121[1102], DS121[1103], DS121[1106], DS121[1107], DS121[1108], DS121[1109], DS121[1110], DS121[1111], DS121[1112], DS121[1115], DS121[1116], DS121[1117], DS121[1118], DS121[1119], DS121[1124], DS121[1125], DS121[1126], DS121[1127], DS121[1128], DS121[1130], DS121[1132], DS121[1133], DS121[1134], DS121[1136], DS121[1137], DS121[1138], DS121[1139], DS121[1140], DS121[1141], DS121[1144], DS121[1145], DS121[1152], DS121[1161], DS121[1162], DS121[1166], DS121[1170], DS121[1175], DS121[1176], DS121[1177], DS121[1178], DS121[1181], DS121[1182], DS121[1191], DS121[1192], DS121[1193], DS121[1194], DS121[1195], DS121[1196], DS121[1213], DS121[1220], DS121[1221], DS121[1235], DS121[1238], DS121[1239], DS121[1240], DS121[1241], DS121[1242], DS121[1243], DS121[1244], DS121[1245], DS121[1246], DS121[1247], DS121[1248], DS121[1249], DS121[1250], DS121[1255], DS121[1258], DS121[1259], DS121[1262], DS121[1265], DS121[1268], DS121[1270], DS121[1273], DS121[1274], DS121[1281], DS121[1282], DS121[1304], DS121[1305], DS121[1307], DS121[1308], DS121[1309], DS121[1310], DS121[1311], DS121[1312], DS121[1315], DS121[1323], DS121[1333], DS121[1336], DS121[1341], DS121[1345], DS121[1348], DS121[1349], DS121[1350], DS121[1352], DS121[1362], DS121[1363], DS121[1364], DS121[1365], DS121[1366], DS121[1368], DS121[1369], DS121[1370], DS121[1372], DS121[1373], DS121[1374], DS121[1375], DS121[1376], DS121[1377], DS121[1378], DS121[1379], DS121[1381], DS121[1382], DS121[1383], DS121[1384], DS121[1385], DS121[1386], DS121[1387], DS121[1388], DS121[1389], DS121[1390], DS121[1391], DS121[1392], DS121[1393], DS121[1394], DS121[1395], DS121[1396], DS121[1397], DS121[1398], DS121[1399], DS121[1400], DS121[1401], DS121[1402], DS121[1403], DS121[1406], DS121[1407], DS121[1408], DS121[1409], DS121[1410], DS121[1411], DS121[1412], DS121[1413], DS121[1414], DS121[1415], DS121[1416], DS121[1417], DS121[1418], DS121[1419], DS121[1420], DS121[1421], DS121[1422], DS121[1423], DS121[1424], DS121[1425], DS121[1426], DS121[1427], DS121[1428], DS121[1429], DS121[1430], DS121[1431], DS121[1432], DS121[1433], DS121[1434], DS121[1435], DS121[1436], DS121[1437], DS121[1438], DS121[1439], DS121[1442], DS121[1443], DS121[1444], DS121[1445], DS121[1446], DS121[1447], DS121[1448], DS121[1449], DS121[1450], DS121[1451], DS121[1452], DS121[1453], DS121[1454], DS121[1455], DS121[1456], DS121[1457], DS121[1458], DS121[1459], DS121[1460], DS121[1461], DS121[1462], DS121[1463], DS121[1464], DS121[1465], DS121[1466], DS121[1467], DS121[1468], DS121[1469], DS121[1470], DS121[1471], DS121[1472], DS121[1473], DS121[1474], DS121[1475], DS121[1476], DS121[1477], DS121[1478], DS121[1479], DS121[1480], DS121[1481], DS121[1482], DS121[1483], DS121[1484], DS121[1485], DS121[1486], DS121[1487], DS121[1488], DS121[1489], DS121[1490], DS121[1491], DS121[1492], DS121[1493], DS121[1494], DS121[1495], DS121[1496], DS121[1497], DS121[1498], DS121[1499], DS121[1500], DS121[1501], DS121[1502], DS121[1503], DS121[1504], DS121[1505], DS121[1506], DS121[1507], DS121[1508], DS121[1509], DS121[1512], DS121[1513], DS121[1514], DS121[1515], DS121[1516], DS121[1517], DS121[1518], DS121[1519], DS121[1520], DS121[1521], DS121[1522], DS121[1523], DS121[1524], DS121[1525], DS121[1526], DS121[1527], DS121[1528], DS121[1529], DS121[1530], DS121[1531], DS121[1532], DS121[1533], DS121[1534], DS121[1535], DS121[1536], DS121[1537], DS121[1538], DS121[1539], DS121[1540], DS121[1541], DS121[1542], DS121[1543], DS121[1544], DS121[1545], DS121[1546], DS121[1547], DS121[1548], DS121[1549], DS121[1550], DS121[1551], DS121[1552], DS121[1553], DS121[1554], DS121[1555], DS121[1556], DS121[1557], DS121[1558], DS121[1559], DS121[1560], DS121[1561], DS121[1562], DS121[1563], DS121[1564], DS121[1565], DS121[1566], DS121[1567], DS121[1568], DS121[1569], DS121[1570], DS121[1571], DS121[1572], DS121[1573], DS121[1574], DS121[1575], DS121[1577], DS121[1578], DS121[1579], DS121[1582], DS121[1583], DS121[1584], DS121[1585], DS121[1586], DS121[1587], DS121[1588], DS121[1589], DS121[1590], DS121[1591], DS121[1592], DS121[1593], DS121[1594], DS121[1595], DS121[1596], DS121[1597], DS121[1598], DS121[1599], DS121[1600], DS121[1602], DS121[1603], DS121[1604], DS121[1605], DS121[1606], DS121[1607], DS121[1608], DS121[1609], DS121[1610], DS121[1611], DS121[1612], DS121[1613], DS121[1614], DS121[1615], DS121[1616], DS121[1617], DS121[1618], DS121[1619], DS121[1620], DS121[1621], DS121[1622], DS121[1623], DS121[1624], DS121[1625], DS121[1626], DS121[1627], DS121[1628], DS121[1629], DS121[1630], DS121[1631], DS121[1632], DS121[1633], DS121[1634], DS121[1635], DS121[1636], DS121[1637], DS121[1638], DS121[1639], DS121[1640], DS121[1641], DS121[1642], DS121[1643], DS121[1644], DS121[1645], DS121[1646], DS121[1647], DS121[1648], DS121[1649], DS121[1650], DS121[1651], DS121[1652], DS121[1653], DS121[1654], DS121[1655], DS121[1656], DS121[1657], DS121[1658], DS121[1659], DS121[1660], DS121[1661], DS121[1662], DS121[1663], DS121[1664], DS121[1665], DS121[1666], DS121[1667], DS121[1668], DS121[1669], DS121[1670], DS121[1671], DS121[1672], DS121[1673], DS121[1674], DS121[1675], DS121[1676], DS121[1677], DS121[1679], DS121[1680], DS121[1681], DS121[1682], DS121[1683], DS121[1684], DS121[1685], DS121[1686], DS121[1687], DS121[1688], DS121[1689], DS121[1690], DS121[1691], DS121[1692], DS121[1693], DS121[1694], DS121[1695], DS121[1697], DS121[1698], DS121[1699], DS121[1705], DS121[1706], DS121[1707], DS121[1708], DS121[1709], DS121[1710], DS121[1711], DS121[1712], DS121[1713], DS121[1714], DS121[1715], DS121[1717], DS121[1718], DS121[1719], DS121[1720], DS121[1721], DS121[1722], DS121[1723], DS121[1724], DS121[1725], DS121[1726], DS121[1727], DS121[1728], DS121[1729], DS121[1730], DS121[1731], DS121[1732], DS121[1733], DS121[1734], DS121[1735], DS121[1737], DS121[1738], DS121[1739], DS121[1740], DS121[1742], DS121[1743], DS121[1744], DS121[1746], DS121[1747], DS121[1748], DS121[1749], DS121[1750], DS121[1751], DS121[1752], DS121[1753], DS121[1754], DS121[1756], DS121[1757], DS121[1758], DS121[1759], DS121[1760], DS121[1761], DS121[1762], DS121[1763], DS121[1764], DS121[1765], DS121[1766], DS121[1767], DS121[1768], DS121[1769], DS121[1770], DS121[1771], DS121[1772], DS121[1773], DS121[1774], DS121[1775], DS121[1776], DS121[1777], DS121[1778], DS121[1779], DS121[1780], DS121[1781], DS121[1782], DS121[1783], DS121[1784], DS121[1785], DS121[1786], DS121[1787], DS121[1788], DS121[1789], DS121[1790], DS121[1791], DS121[1792], DS121[1793], DS121[1794], DS121[1795], DS121[1796], DS121[1797], DS121[1798], DS121[1799], DS121[1800], DS121[1801], DS121[1802], DS121[1803], DS121[1804], DS121[1805], DS121[1806], DS121[1807], DS121[1808]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,121].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,121] is 64
### The list of all inequivalent reversible (64,28,12) DSs in group [64,121] is 
  
  
RDS121:=[ [ 3, 6, 8, 9, 13, 14, 17, 20, 22, 24, 25, 29, 34, 38, 39, 40, 42, 43, 44, 45, 46, 49, 54, 56, 57, 62, 63, 64 ], [ 3, 6, 8, 9, 13, 14, 17, 20, 22, 23, 24, 25, 29, 34, 38, 39, 40, 42, 46, 49, 54, 56, 57, 58, 59, 60, 62, 63 ], [ 3, 6, 8, 9, 13, 14, 17, 20, 22, 23, 24, 25, 29, 33, 34, 38, 39, 40, 42, 46, 49, 53, 56, 57, 58, 59, 60, 62 ], [ 3, 6, 8, 9, 13, 14, 15, 17, 20, 22, 23, 29, 34, 36, 39, 40, 42, 46, 47, 48, 49, 54, 57, 58, 59, 60, 62, 63 ], [ 3, 5, 6, 8, 9, 13, 14, 17, 21, 22, 24, 25, 27, 29, 34, 38, 39, 40, 43, 44, 45, 46, 50, 54, 56, 57, 63, 64 ], [ 3, 5, 6, 8, 9, 13, 14, 17, 21, 22, 23, 24, 25, 27, 29, 34, 38, 39, 40, 46, 50, 54, 56, 57, 58, 59, 60, 63 ], [ 3, 5, 6, 8, 9, 13, 14, 17, 21, 22, 23, 24, 25, 27, 29, 33, 34, 38, 39, 40, 46, 50, 53, 56, 57, 58, 59, 60 ], [ 3, 5, 6, 8, 9, 13, 14, 15, 17, 21, 22, 23, 27, 29, 34, 36, 39, 40, 46, 47, 48, 50, 54, 57, 58, 59, 60, 63 ], [ 3, 4, 6, 8, 9, 13, 14, 18, 19, 20, 22, 24, 25, 29, 34, 38, 41, 42, 43, 44, 45, 46, 49, 54, 56, 62, 63, 64 ], [ 3, 4, 6, 8, 9, 13, 14, 18, 19, 20, 22, 23, 24, 25, 29, 34, 38, 41, 42, 46, 49, 54, 56, 58, 59, 60, 62, 63 ], [ 3, 4, 6, 8, 9, 13, 14, 18, 19, 20, 22, 23, 24, 25, 29, 33, 34, 38, 41, 42, 46, 49, 53, 56, 58, 59, 60, 62 ], [ 3, 4, 6, 8, 9, 13, 14, 15, 18, 19, 20, 22, 23, 29, 34, 36, 41, 42, 46, 47, 48, 49, 54, 58, 59, 60, 62, 63 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 18, 19, 21, 22, 24, 25, 27, 29, 34, 38, 41, 43, 44, 45, 46, 50, 54, 56, 63, 64 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 18, 19, 21, 22, 23, 24, 25, 27, 29, 34, 38, 41, 46, 50, 54, 56, 58, 59, 60, 63 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 18, 19, 21, 22, 23, 24, 25, 27, 29, 33, 34, 38, 41, 46, 50, 53, 56, 58, 59, 60 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 15, 18, 19, 21, 22, 23, 27, 29, 34, 36, 41, 46, 47, 48, 50, 54, 58, 59, 60, 63 ], [ 2, 3, 6, 8, 9, 11, 12, 13, 20, 22, 24, 25, 29, 32, 33, 34, 36, 37, 38, 42, 43, 44, 45, 46, 49, 53, 62, 64 ], [ 2, 3, 6, 8, 9, 11, 12, 13, 20, 22, 23, 24, 25, 29, 32, 34, 36, 37, 38, 42, 46, 49, 54, 58, 59, 60, 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