### 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 [64,172]. 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 [64,172].
    
    
# 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(64,172));' can be 
# used to create a list e of the elements of the group [64,172].
# In our list of (64,28,12) DSs in group [64,172], we have [1, 
# 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 21, 23, 26, 28, 
# 29, 30, 31, 40, 41, 43, 46, 51, 56, 57, 58, 60, 61].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[7], e[8], e[9], e[11], e[14], e[15], e[21], e[23], e[26], e[28], e[29], 
# e[30], e[31], e[40], e[41], e[43], e[46], e[51], e[56], e[57], e[58], e[60], e[61]]
# where e is the list of the elements of the group [64,172] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,172));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 172]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,172] is 1092
### The list of all inequivalent (64,28,12) DSs in group [64,172] is 
  
  
DS172:=[ [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 21, 23, 26, 28, 29, 30, 31, 40, 41, 43, 46, 51, 56, 57, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 15, 21, 23, 25, 26, 29, 30, 32, 40, 41, 44, 48, 49, 56, 57, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 16, 18, 19, 23, 29, 30, 31, 34, 37, 41, 42, 49, 53, 54, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 16, 18, 19, 23, 29, 30, 31, 33, 37, 41, 42, 49, 53, 55, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 16, 17, 19, 23, 28, 29, 30, 32, 33, 36, 40, 42, 51, 53, 55, 56, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 16, 17, 19, 23, 28, 29, 30, 32, 33, 36, 40, 42, 43, 44, 51, 53, 55, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 16, 19, 28, 29, 30, 32, 34, 37, 39, 42, 43, 44, 45, 51, 53, 54, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 16, 19, 23, 28, 29, 30, 32, 34, 37, 39, 42, 51, 53, 54, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 16, 19, 23, 28, 29, 30, 32, 34, 37, 39, 42, 43, 44, 51, 53, 54, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 18, 19, 27, 29, 34, 36, 41, 42, 43, 45, 50, 52, 53, 54, 56, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 18, 19, 23, 27, 29, 34, 36, 41, 42, 44, 50, 52, 53, 54, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 18, 19, 23, 27, 29, 34, 36, 41, 42, 43, 50, 52, 53, 54, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 17, 19, 28, 29, 34, 36, 40, 42, 43, 45, 51, 52, 53, 54, 56, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 17, 19, 28, 29, 33, 36, 40, 42, 44, 45, 51, 52, 53, 55, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 17, 19, 23, 28, 29, 34, 36, 40, 42, 44, 51, 52, 53, 54, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 17, 19, 23, 28, 29, 34, 36, 40, 42, 43, 51, 52, 53, 54, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 17, 19, 23, 28, 29, 33, 36, 40, 42, 44, 51, 52, 53, 55, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 16, 17, 19, 23, 28, 29, 33, 36, 40, 42, 43, 51, 52, 53, 55, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 18, 23, 28, 29, 35, 36, 37, 39, 40, 42, 43, 45, 51, 52, 53, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 18, 23, 27, 29, 35, 36, 37, 39, 40, 42, 44, 45, 50, 52, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 18, 19, 23, 27, 29, 35, 36, 37, 41, 42, 44, 50, 52, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 18, 19, 23, 27, 29, 35, 36, 37, 41, 42, 43, 50, 52, 53, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 17, 19, 23, 28, 29, 35, 36, 37, 40, 42, 44, 51, 52, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 17, 19, 23, 28, 29, 35, 36, 37, 40, 42, 43, 51, 52, 53, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 16, 19, 23, 27, 29, 33, 38, 39, 42, 44, 50, 52, 53, 55, 57, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 16, 19, 23, 27, 29, 33, 38, 39, 42, 43, 50, 52, 53, 55, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 16, 17, 19, 23, 29, 34, 38, 40, 42, 43, 49, 52, 53, 54, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 15, 16, 17, 19, 23, 29, 33, 38, 40, 42, 43, 49, 52, 53, 55, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 19, 23, 28, 29, 34, 37, 39, 42, 44, 51, 52, 53, 54, 57, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 19, 23, 28, 29, 34, 37, 39, 42, 43, 51, 52, 53, 54, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 19, 23, 28, 29, 33, 37, 39, 42, 44, 51, 52, 53, 55, 57, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 19, 23, 28, 29, 33, 37, 39, 42, 43, 51, 52, 53, 55, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 18, 19, 23, 29, 34, 37, 41, 42, 44, 49, 52, 53, 54, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 18, 19, 23, 29, 34, 37, 41, 42, 43, 49, 52, 53, 54, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 18, 19, 23, 29, 33, 37, 41, 42, 44, 49, 52, 53, 55, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 18, 19, 23, 29, 33, 37, 41, 42, 43, 49, 52, 53, 55, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 15, 16, 17, 19, 23, 26, 30, 31, 33, 34, 38, 40, 42, 43, 46, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 19, 23, 26, 30, 31, 33, 34, 37, 41, 42, 43, 46, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 18, 19, 23, 24, 26, 30, 32, 33, 34, 36, 41, 42, 44, 47, 56, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 17, 19, 25, 26, 30, 32, 33, 36, 40, 42, 45, 48, 53, 55, 56, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 17, 19, 23, 25, 26, 30, 32, 33, 36, 40, 42, 48, 53, 55, 56, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 17, 19, 23, 25, 26, 30, 32, 33, 36, 40, 42, 43, 44, 48, 53, 55, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 17, 19, 23, 25, 26, 30, 32, 33, 34, 36, 40, 42, 44, 48, 56, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 15, 16, 19, 23, 24, 26, 30, 32, 33, 34, 38, 39, 42, 44, 47, 57, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 15, 16, 17, 19, 23, 26, 30, 32, 33, 34, 38, 40, 42, 44, 46, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 19, 23, 25, 26, 30, 32, 34, 37, 39, 42, 48, 53, 54, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 19, 23, 25, 26, 30, 32, 34, 37, 39, 42, 43, 44, 48, 53, 54, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 19, 23, 25, 26, 30, 32, 33, 34, 37, 39, 42, 44, 48, 57, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 18, 19, 23, 26, 30, 32, 34, 37, 41, 42, 46, 53, 54, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 18, 19, 23, 26, 30, 32, 33, 37, 41, 42, 46, 53, 55, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 18, 19, 23, 26, 30, 32, 33, 34, 37, 41, 42, 44, 46, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 18, 19, 23, 24, 26, 34, 36, 41, 42, 44, 47, 52, 53, 54, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 18, 19, 23, 24, 26, 34, 36, 41, 42, 43, 47, 52, 53, 54, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 17, 19, 23, 25, 26, 34, 36, 40, 42, 44, 48, 52, 53, 54, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 17, 19, 23, 25, 26, 34, 36, 40, 42, 43, 48, 52, 53, 54, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 17, 19, 23, 25, 26, 33, 36, 40, 42, 44, 48, 52, 53, 55, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 17, 19, 23, 25, 26, 33, 36, 40, 42, 43, 48, 52, 53, 55, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 17, 19, 20, 25, 26, 30, 33, 36, 40, 44, 45, 48, 55, 56, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 17, 19, 20, 25, 26, 30, 33, 34, 36, 40, 45, 48, 53, 56, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16, 19, 24, 26, 33, 38, 39, 42, 44, 45, 47, 52, 53, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16, 19, 23, 24, 26, 33, 38, 39, 42, 44, 47, 52, 53, 55, 57, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16, 19, 23, 24, 26, 33, 38, 39, 42, 43, 47, 52, 53, 55, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16, 19, 20, 24, 26, 30, 33, 38, 39, 44, 45, 47, 55, 57, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16, 19, 20, 24, 26, 30, 33, 34, 38, 39, 45, 47, 53, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16, 17, 19, 23, 26, 34, 38, 40, 42, 44, 46, 52, 53, 54, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16, 17, 19, 23, 26, 33, 38, 40, 42, 44, 46, 52, 53, 55, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 18, 19, 23, 24, 26, 35, 36, 38, 41, 42, 44, 47, 52, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 18, 19, 23, 24, 26, 35, 36, 38, 41, 42, 43, 47, 52, 53, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 17, 23, 25, 26, 35, 36, 38, 39, 41, 42, 43, 45, 48, 52, 53, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 17, 23, 24, 26, 35, 36, 38, 39, 41, 42, 44, 45, 47, 52, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 17, 19, 23, 25, 26, 35, 36, 38, 40, 42, 44, 48, 52, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 17, 19, 23, 25, 26, 35, 36, 38, 40, 42, 43, 48, 52, 53, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 16, 19, 25, 26, 34, 37, 39, 42, 43, 45, 48, 52, 53, 54, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 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12, 14, 15, 19, 20, 25, 34, 37, 40, 42, 43, 51, 54, 57, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 19, 20, 25, 33, 37, 40, 42, 44, 51, 55, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 22, 28, 35, 36, 39, 40, 42, 43, 44, 47, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 25, 26, 29, 30, 34, 37, 40, 45, 46, 51, 52, 53, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 25, 26, 29, 37, 40, 42, 43, 45, 46, 51, 53, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 24, 25, 27, 32, 35, 37, 45, 46, 49, 50, 52, 53, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 24, 30, 33, 36, 38, 41, 45, 50, 52, 53, 54, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 20, 24, 36, 38, 41, 42, 44, 45, 50, 53, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 24, 31, 32, 33, 34, 36, 39, 40, 43, 51, 53, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 21, 24, 34, 36, 38, 39, 42, 45, 51, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 21, 24, 34, 36, 38, 39, 42, 43, 44, 45, 51, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 26, 29, 30, 34, 36, 37, 39, 40, 45, 52, 55, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 26, 29, 30, 33, 36, 37, 39, 40, 45, 52, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 23, 30, 34, 36, 39, 40, 47, 50, 52, 53, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 20, 23, 36, 39, 40, 42, 44, 47, 50, 53, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 19, 30, 33, 36, 41, 45, 47, 50, 52, 53, 54, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 19, 20, 36, 41, 42, 44, 45, 47, 50, 53, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 26, 29, 30, 34, 40, 45, 46, 48, 51, 52, 53, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 23, 25, 26, 30, 34, 40, 49, 50, 52, 53, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 26, 29, 40, 42, 43, 45, 46, 48, 51, 53, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 24, 29, 40, 42, 44, 45, 46, 51, 53, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 24, 30, 34, 36, 41, 45, 50, 52, 53, 55, 56, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 20, 24, 36, 41, 42, 44, 45, 50, 53, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 20, 36, 37, 39, 41, 42, 44, 45, 46, 49, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 20, 36, 37, 39, 41, 42, 43, 45, 46, 49, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 26, 29, 30, 34, 36, 38, 39, 41, 45, 52, 55, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 26, 29, 30, 33, 36, 38, 39, 41, 45, 52, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 20, 36, 37, 39, 40, 42, 44, 45, 46, 49, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 20, 36, 37, 39, 40, 42, 43, 45, 46, 49, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 19, 20, 38, 40, 42, 44, 45, 46, 49, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 19, 20, 38, 40, 42, 43, 45, 46, 49, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 20, 38, 41, 42, 44, 45, 46, 49, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 20, 38, 41, 42, 43, 45, 46, 49, 58, 59, 63 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 767
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS172[2], DS172[7], DS172[8], DS172[16], DS172[19], DS172[20], DS172[21], DS172[22], DS172[23], DS172[24], DS172[29], DS172[41], DS172[45], DS172[47], DS172[50], DS172[54], DS172[55], DS172[59], DS172[62], DS172[64], DS172[65], DS172[66], DS172[67], DS172[68], DS172[69], DS172[70], DS172[71], DS172[72], DS172[78], DS172[79], DS172[80], DS172[86], DS172[88], DS172[89], DS172[100], DS172[107], DS172[108], DS172[110], DS172[113], DS172[114], DS172[116], DS172[118], DS172[119], DS172[122], DS172[123], DS172[128], DS172[129], DS172[130], DS172[131], DS172[134], DS172[138], DS172[141], DS172[142], DS172[143], DS172[144], DS172[145], DS172[147], DS172[150], DS172[154], DS172[155], DS172[157], DS172[158], DS172[160], DS172[161], DS172[162], DS172[164], DS172[165], DS172[166], DS172[170], DS172[171], DS172[172], DS172[173], DS172[174], DS172[175], DS172[178], DS172[180], DS172[181], DS172[182], DS172[183], DS172[184], DS172[185], DS172[186], DS172[187], DS172[188], DS172[189], DS172[190], DS172[191], DS172[192], DS172[193], DS172[194], DS172[195], DS172[196], DS172[197], DS172[198], DS172[199], DS172[202], DS172[205], DS172[206], DS172[209], DS172[211], DS172[212], DS172[213], DS172[215], DS172[216], DS172[218], DS172[219], DS172[220], DS172[221], DS172[225], DS172[226], DS172[228], DS172[232], DS172[233], DS172[234], DS172[235], DS172[236], DS172[238], DS172[239], DS172[240], DS172[241], DS172[242], DS172[243], DS172[244], DS172[246], DS172[247], DS172[248], DS172[249], DS172[250], DS172[252], DS172[253], DS172[256], DS172[257], DS172[261], DS172[262], DS172[263], DS172[265], DS172[266], DS172[270], DS172[276], DS172[277], DS172[281], DS172[283], DS172[284], DS172[285], DS172[286], DS172[287], DS172[289], DS172[290], DS172[291], DS172[293], DS172[296], DS172[297], DS172[298], DS172[299], DS172[300], DS172[301], DS172[302], DS172[303], DS172[305], DS172[306], DS172[308], DS172[311], DS172[312], DS172[314], DS172[315], DS172[316], DS172[317], DS172[318], DS172[319], DS172[320], DS172[322], DS172[323], DS172[324], DS172[325], DS172[326], DS172[327], DS172[328], DS172[329], DS172[330], DS172[331], DS172[332], DS172[333], DS172[334], DS172[335], DS172[337], DS172[338], DS172[339], DS172[340], DS172[341], DS172[342], DS172[343], DS172[344], DS172[345], DS172[346], DS172[347], DS172[348], DS172[349], DS172[350], DS172[351], DS172[352], DS172[353], DS172[354], DS172[363], DS172[365], DS172[366], DS172[367], DS172[368], DS172[371], DS172[373], DS172[384], DS172[385], DS172[386], DS172[388], DS172[389], DS172[390], DS172[391], DS172[394], DS172[399], DS172[400], DS172[402], DS172[403], DS172[404], DS172[408], DS172[410], DS172[415], DS172[417], DS172[418], DS172[419], DS172[420], DS172[423], DS172[427], DS172[429], DS172[432], DS172[433], DS172[437], DS172[438], DS172[439], DS172[440], DS172[441], DS172[442], DS172[443], DS172[445], DS172[446], DS172[447], DS172[448], DS172[452], DS172[453], DS172[456], DS172[457], DS172[458], DS172[459], DS172[463], DS172[471], DS172[472], DS172[473], DS172[474], DS172[489], DS172[490], DS172[495], DS172[496], DS172[501], DS172[503], DS172[507], DS172[514], DS172[516], DS172[519], DS172[524], DS172[525], DS172[530], DS172[541], DS172[550], DS172[551], DS172[552], DS172[553], DS172[554], DS172[555], DS172[556], DS172[557], DS172[560], DS172[566], DS172[567], DS172[575], DS172[580], DS172[581], DS172[583], DS172[584], DS172[585], DS172[587], DS172[588], DS172[593], DS172[594], DS172[595], DS172[596], DS172[597], DS172[598], DS172[599], DS172[600], DS172[601], DS172[602], DS172[603], DS172[604], DS172[605], DS172[606], DS172[607], DS172[608], DS172[609], DS172[610], DS172[611], DS172[612], DS172[613], DS172[614], DS172[615], DS172[616], DS172[617], DS172[618], DS172[620], DS172[622], DS172[623], DS172[626], DS172[628], DS172[631], DS172[632], DS172[633], DS172[634], DS172[635], DS172[636], DS172[637], DS172[638], DS172[639], DS172[640], DS172[641], DS172[642], DS172[643], DS172[644], DS172[645], DS172[646], DS172[647], DS172[649], DS172[650], DS172[651], DS172[652], DS172[653], DS172[654], DS172[655], DS172[657], DS172[658], DS172[659], DS172[660], DS172[661], DS172[662], DS172[663], DS172[664], DS172[665], DS172[666], DS172[667], DS172[668], DS172[669], DS172[670], DS172[671], DS172[672], DS172[673], DS172[674], DS172[675], DS172[676], DS172[677], DS172[678], DS172[679], DS172[680], DS172[681], DS172[682], DS172[683], DS172[684], DS172[685], DS172[686], DS172[687], DS172[688], DS172[689], DS172[690], DS172[691], DS172[692], DS172[693], DS172[694], DS172[695], DS172[696], DS172[697], DS172[698], DS172[699], DS172[700], DS172[701], DS172[702], DS172[703], DS172[704], DS172[705], DS172[706], DS172[707], DS172[708], DS172[709], DS172[710], DS172[711], DS172[712], DS172[713], DS172[714], DS172[715], DS172[716], DS172[717], DS172[718], DS172[719], DS172[720], DS172[721], DS172[722], DS172[723], DS172[724], DS172[725], DS172[726], DS172[727], DS172[728], DS172[729], DS172[730], DS172[731], DS172[732], DS172[733], DS172[734], DS172[735], DS172[736], DS172[737], DS172[738], DS172[739], DS172[741], DS172[742], DS172[743], DS172[744], DS172[745], DS172[746], DS172[747], DS172[748], DS172[749], DS172[750], DS172[751], DS172[752], DS172[753], DS172[754], DS172[755], DS172[756], DS172[757], DS172[758], DS172[759], DS172[760], DS172[761], DS172[763], DS172[764], DS172[766], DS172[768], DS172[770], DS172[771], DS172[772], DS172[773], DS172[774], DS172[775], DS172[776], DS172[777], DS172[778], DS172[779], DS172[780], DS172[781], DS172[782], DS172[783], DS172[784], DS172[785], DS172[786], DS172[787], DS172[788], DS172[789], DS172[790], DS172[791], DS172[792], DS172[793], DS172[794], DS172[795], DS172[796], DS172[797], DS172[798], DS172[799], DS172[800], DS172[801], DS172[802], DS172[803], DS172[804], DS172[805], DS172[806], DS172[807], DS172[808], DS172[809], DS172[810], DS172[811], DS172[812], DS172[813], DS172[814], DS172[815], DS172[816], DS172[817], DS172[818], DS172[819], DS172[820], DS172[821], DS172[822], DS172[823], DS172[824], DS172[825], DS172[826], DS172[829], DS172[830], DS172[831], DS172[832], DS172[833], DS172[834], DS172[835], DS172[836], DS172[837], DS172[838], DS172[839], DS172[840], DS172[841], DS172[842], DS172[843], DS172[844], DS172[845], DS172[846], DS172[847], DS172[848], DS172[849], DS172[850], DS172[851], DS172[852], DS172[853], DS172[854], DS172[855], DS172[856], DS172[857], DS172[858], DS172[859], DS172[862], DS172[863], DS172[864], DS172[865], DS172[866], DS172[867], DS172[868], DS172[869], DS172[870], DS172[871], DS172[872], DS172[873], DS172[874], DS172[875], DS172[876], DS172[877], DS172[878], DS172[879], DS172[880], DS172[881], DS172[882], DS172[883], DS172[884], DS172[885], DS172[886], DS172[887], DS172[888], DS172[889], DS172[890], DS172[891], DS172[892], DS172[893], DS172[894], DS172[895], DS172[896], DS172[897], DS172[898], DS172[899], DS172[900], DS172[901], DS172[902], DS172[903], DS172[904], DS172[905], DS172[906], DS172[907], DS172[908], DS172[909], DS172[910], DS172[911], DS172[912], DS172[913], DS172[914], DS172[915], DS172[916], DS172[917], DS172[918], DS172[919], DS172[920], DS172[921], DS172[922], DS172[923], DS172[924], DS172[925], DS172[926], DS172[927], DS172[928], DS172[929], DS172[932], DS172[933], DS172[934], DS172[935], DS172[936], DS172[937], DS172[938], DS172[939], DS172[940], DS172[941], DS172[942], DS172[943], DS172[944], DS172[945], DS172[946], DS172[947], DS172[948], DS172[949], DS172[950], DS172[951], DS172[952], DS172[953], DS172[954], DS172[955], DS172[956], DS172[957], DS172[958], DS172[959], DS172[960], DS172[961], DS172[962], DS172[963], DS172[964], DS172[965], DS172[966], DS172[967], DS172[968], DS172[969], DS172[970], DS172[971], DS172[972], DS172[973], DS172[974], DS172[975], DS172[976], DS172[977], DS172[978], DS172[979], DS172[980], DS172[981], DS172[982], DS172[983], DS172[984], DS172[985], DS172[986], DS172[987], DS172[988], DS172[989], DS172[990], DS172[991], DS172[992], DS172[993], DS172[994], DS172[995], DS172[996], DS172[997], DS172[998], DS172[999], DS172[1000], DS172[1001], DS172[1002], DS172[1003], DS172[1004], DS172[1005], DS172[1006], DS172[1007], DS172[1008], DS172[1009], DS172[1010], DS172[1011], DS172[1012], DS172[1013], DS172[1014], DS172[1015], DS172[1016], DS172[1017], DS172[1018], DS172[1019], DS172[1020], DS172[1021], DS172[1022], DS172[1023], DS172[1024], DS172[1025], DS172[1026], DS172[1027], DS172[1028], DS172[1029], DS172[1030], DS172[1031], DS172[1032], DS172[1033], DS172[1034], DS172[1035], DS172[1036], DS172[1037], DS172[1038], DS172[1039], DS172[1040], DS172[1041], DS172[1042], DS172[1043], DS172[1044], DS172[1045], DS172[1046], DS172[1047], DS172[1048], DS172[1049], DS172[1050], DS172[1051], DS172[1052], DS172[1053], DS172[1054], DS172[1055], DS172[1056], DS172[1057], DS172[1058], DS172[1059], DS172[1060], DS172[1061], DS172[1062], DS172[1063], DS172[1064], DS172[1065], DS172[1066], DS172[1067], DS172[1068], DS172[1069], DS172[1070], DS172[1071], DS172[1073], DS172[1074], DS172[1075], DS172[1076], DS172[1077], DS172[1078], DS172[1079], DS172[1080], DS172[1081], DS172[1082], DS172[1083], DS172[1084], DS172[1085], DS172[1087], DS172[1088], DS172[1089], DS172[1090], DS172[1091], DS172[1092]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,172].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,172] is 52
### The list of all inequivalent reversible (64,28,12) DSs in group [64,172] is 
  
  
RDS172:=[ [ 2, 3, 4, 8, 9, 10, 12, 14, 15, 18, 24, 31, 33, 34, 39, 40, 43, 46, 48, 50, 51, 54, 55, 56, 58, 59, 62, 64 ], [ 2, 3, 4, 8, 9, 10, 12, 14, 15, 18, 23, 24, 31, 33, 34, 39, 40, 44, 45, 46, 48, 50, 51, 54, 55, 56, 60, 62 ], [ 2, 3, 4, 8, 9, 10, 12, 14, 15, 18, 23, 24, 27, 28, 31, 33, 34, 39, 40, 44, 45, 46, 48, 54, 55, 56, 60, 62 ], [ 2, 3, 4, 8, 9, 10, 12, 13, 14, 15, 18, 24, 31, 35, 39, 40, 43, 46, 48, 50, 51, 53, 56, 58, 59, 62, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 12, 13, 14, 15, 18, 23, 24, 31, 35, 39, 40, 44, 45, 46, 48, 50, 51, 53, 56, 60, 62, 63 ], [ 2, 3, 4, 8, 9, 10, 12, 13, 14, 15, 18, 23, 24, 27, 28, 31, 35, 39, 40, 44, 45, 46, 48, 53, 56, 60, 62, 63 ], [ 2, 3, 4, 5, 8, 10, 12, 15, 20, 21, 24, 29, 31, 33, 34, 36, 37, 40, 41, 42, 46, 48, 49, 50, 51, 54, 55, 57 ], [ 2, 3, 4, 5, 8, 10, 12, 13, 15, 20, 21, 24, 29, 31, 35, 36, 37, 40, 41, 42, 46, 48, 49, 50, 51, 53, 57, 63 ], [ 2, 3, 4, 5, 8, 9, 12, 14, 15, 18, 20, 21, 25, 27, 28, 30, 39, 40, 42, 44, 46, 47, 52, 56, 58, 60, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 12, 14, 15, 18, 20, 21, 23, 24, 30, 39, 40, 42, 43, 45, 46, 48, 50, 51, 52, 56, 59, 62 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 24, 31, 33, 34, 36, 37, 40, 41, 42, 46, 48, 50, 51, 54, 55, 57, 62 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 24, 27, 28, 31, 33, 34, 36, 37, 40, 41, 42, 46, 48, 54, 55, 57, 62 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 25, 31, 36, 37, 40, 41, 42, 45, 46, 47, 50, 51, 57, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 25, 27, 28, 31, 36, 37, 40, 41, 42, 45, 46, 47, 57, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 24, 31, 36, 37, 40, 41, 42, 45, 46, 48, 50, 51, 57, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 15, 20, 21, 23, 24, 27, 28, 31, 36, 37, 40, 41, 42, 45, 46, 48, 57, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 31, 33, 34, 39, 40, 42, 46, 48, 50, 51, 54, 55, 56, 62 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 31, 33, 34, 39, 40, 42, 46, 48, 54, 55, 56, 62 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 21, 23, 25, 31, 39, 40, 42, 45, 46, 47, 50, 51, 56, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 21, 23, 25, 27, 28, 31, 39, 40, 42, 45, 46, 47, 56, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 21, 23, 24, 31, 39, 40, 42, 45, 46, 48, 50, 51, 56, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 14, 15, 18, 20, 21, 23, 24, 27, 28, 31, 39, 40, 42, 45, 46, 48, 56, 58, 62, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 13, 15, 20, 21, 24, 31, 35, 36, 37, 40, 41, 42, 46, 48, 50, 51, 53, 57, 62, 63 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 13, 15, 20, 21, 24, 27, 28, 31, 35, 36, 37, 40, 41, 42, 46, 48, 53, 57, 62, 63 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 18, 20, 21, 24, 31, 35, 39, 40, 42, 46, 48, 50, 51, 53, 56, 62, 63 ], [ 2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 18, 20, 21, 24, 27, 28, 31, 35, 39, 40, 42, 46, 48, 53, 56, 62, 63 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 22, 24, 31, 39, 40, 43, 46, 48, 50, 51, 56, 58, 59, 62, 64 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 22, 23, 24, 31, 39, 40, 44, 45, 46, 48, 50, 51, 56, 60, 62 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 22, 23, 24, 27, 28, 31, 39, 40, 44, 45, 46, 48, 56, 60, 62 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, 31, 39, 40, 42, 43, 46, 48, 50, 51, 56, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 12, 14, 15, 18, 20, 23, 24, 31, 39, 40, 42, 44, 45, 46, 48, 50, 51, 56, 60, 62 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 12, 14, 15, 18, 20, 23, 24, 27, 28, 31, 39, 40, 42, 44, 45, 46, 48, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 25, 32, 36, 37, 40, 41, 43, 44, 46, 47, 50, 51, 57, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 25, 32, 33, 34, 36, 37, 40, 41, 46, 47, 50, 51, 54, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 24, 32, 33, 34, 36, 37, 40, 41, 46, 48, 50, 51, 54, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 21, 24, 27, 28, 32, 36, 37, 40, 41, 43, 44, 46, 48, 57, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 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