### 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 [64,179]. 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 [64,179].
    
    
# 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(64,179));' can be 
# used to create a list e of the elements of the group [64,179].
# In our list of (64,28,12) DSs in group [64,179], we have [1, 
# 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 29, 
# 32, 34, 38, 40, 43, 45, 49, 54, 56, 57, 59, 62, 63].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[6], e[9], e[11], e[12], e[13], e[14], e[18], e[20], e[23], e[29], e[32], 
# e[34], e[38], e[40], e[43], e[45], e[49], e[54], e[56], e[57], e[59], e[62], e[63]]
# where e is the list of the elements of the group [64,179] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,179));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 179]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,179] is 388
### The list of all inequivalent (64,28,12) DSs in group [64,179] is 
  
  
DS179:=[ [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 29, 32, 34, 38, 40, 43, 45, 49, 54, 56, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 27, 29, 32, 34, 38, 40, 45, 50, 54, 56, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 16, 18, 22, 23, 27, 28, 31, 36, 40, 41, 49, 53, 54, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 16, 18, 20, 23, 28, 31, 35, 38, 40, 43, 44, 50, 53, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 16, 18, 20, 23, 27, 28, 31, 35, 38, 40, 49, 53, 57, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 20, 28, 29, 31, 34, 38, 40, 43, 44, 51, 54, 56, 57, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 20, 23, 29, 31, 34, 38, 40, 44, 45, 49, 54, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 20, 23, 28, 29, 31, 34, 38, 40, 45, 51, 54, 56, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 19, 20, 23, 29, 31, 34, 38, 41, 49, 54, 56, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 19, 20, 23, 28, 31, 34, 38, 41, 45, 50, 54, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 18, 20, 25, 26, 27, 29, 30, 34, 38, 40, 48, 50, 52, 54, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 16, 18, 20, 25, 26, 27, 28, 30, 34, 37, 40, 48, 49, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 17, 19, 20, 23, 26, 27, 28, 31, 36, 37, 38, 40, 44, 45, 46, 49, 52, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 16, 18, 19, 20, 25, 27, 28, 31, 36, 41, 44, 47, 49, 52, 56, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 16, 18, 19, 20, 23, 25, 27, 28, 31, 36, 41, 43, 45, 47, 49, 52, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 16, 17, 19, 20, 23, 25, 27, 28, 31, 36, 40, 44, 45, 47, 49, 52, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 17, 19, 20, 23, 26, 28, 29, 31, 37, 40, 43, 44, 46, 51, 52, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 17, 19, 20, 23, 26, 27, 28, 31, 37, 40, 44, 45, 46, 49, 52, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 19, 20, 25, 27, 28, 31, 38, 39, 44, 47, 49, 52, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 19, 20, 23, 25, 27, 28, 31, 38, 39, 43, 45, 47, 49, 52, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 29, 31, 36, 40, 43, 47, 51, 52, 58, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 29, 31, 36, 40, 43, 44, 47, 51, 52, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 28, 29, 31, 36, 40, 43, 47, 49, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 28, 29, 31, 36, 40, 43, 44, 47, 49, 52, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 27, 31, 36, 40, 45, 47, 49, 52, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 27, 31, 36, 40, 44, 45, 47, 49, 52, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 27, 28, 31, 36, 40, 45, 47, 51, 52, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 22, 23, 25, 27, 28, 31, 36, 40, 44, 45, 47, 51, 52, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 20, 23, 25, 27, 28, 31, 38, 40, 45, 47, 49, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 18, 19, 20, 25, 29, 31, 38, 41, 44, 47, 49, 52, 56, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 18, 19, 20, 23, 25, 27, 29, 31, 38, 41, 45, 47, 50, 52, 56, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 17, 19, 20, 23, 25, 28, 29, 31, 38, 40, 45, 47, 51, 52, 56, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 19, 20, 23, 25, 27, 31, 37, 39, 44, 45, 47, 51, 52, 57, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 19, 20, 23, 25, 27, 28, 31, 37, 39, 44, 45, 47, 49, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 18, 19, 20, 23, 25, 27, 31, 37, 41, 45, 47, 51, 52, 58, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 18, 19, 20, 23, 25, 27, 28, 31, 37, 41, 45, 47, 49, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 15, 17, 19, 22, 25, 27, 28, 31, 38, 40, 44, 45, 47, 51, 52, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 15, 17, 19, 22, 23, 25, 28, 29, 31, 38, 40, 45, 47, 49, 52, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 17, 19, 20, 23, 25, 27, 28, 32, 36, 37, 38, 40, 45, 47, 49, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 17, 19, 20, 23, 25, 26, 27, 36, 37, 38, 40, 44, 45, 49, 52, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 23, 26, 28, 32, 36, 37, 40, 42, 43, 44, 46, 49, 50, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 23, 26, 27, 32, 36, 37, 40, 42, 44, 46, 49, 51, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 20, 23, 25, 29, 32, 37, 40, 43, 44, 47, 49, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 20, 23, 25, 27, 28, 32, 37, 40, 45, 47, 49, 56, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 20, 23, 25, 26, 27, 37, 40, 45, 49, 52, 56, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 20, 23, 25, 26, 27, 37, 40, 44, 45, 49, 52, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 18, 20, 26, 27, 29, 32, 33, 35, 38, 40, 46, 50, 53, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 18, 20, 23, 26, 28, 32, 38, 40, 43, 45, 46, 50, 56, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 18, 20, 23, 26, 27, 29, 32, 38, 40, 44, 46, 50, 56, 57, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 17, 19, 20, 23, 26, 28, 32, 38, 40, 44, 46, 50, 56, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 26, 27, 29, 34, 35, 41, 42, 46, 48, 50, 52, 54, 55, 56 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 25, 26, 27, 29, 34, 35, 41, 42, 50, 52, 54, 55, 56, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 18, 20, 26, 27, 29, 32, 34, 38, 40, 46, 50, 54, 56, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 20, 27, 28, 34, 35, 37, 39, 40, 46, 47, 49, 52, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 19, 20, 25, 27, 28, 34, 37, 39, 41, 47, 48, 49, 52, 54, 55 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 20, 26, 27, 29, 35, 42, 43, 47, 58, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 26, 28, 34, 36, 39, 40, 41, 43, 44, 47, 54, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 20, 26, 34, 35, 40, 42, 43, 47, 53, 57, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 20, 26, 28, 34, 40, 41, 42, 43, 44, 47, 53, 54, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 26, 36, 39, 40, 41, 43, 47, 54, 56, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 26, 34, 35, 36, 40, 41, 43, 47, 56, 57, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 26, 28, 35, 36, 39, 40, 43, 44, 47, 56, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 27, 32, 37, 41, 44, 49, 50, 52, 56, 59, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 27, 32, 34, 37, 39, 44, 50, 51, 52, 56, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 27, 28, 32, 34, 37, 39, 44, 45, 50, 52, 56, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 29, 30, 37, 41, 43, 44, 50, 52, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 28, 30, 37, 41, 43, 45, 49, 52, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 28, 30, 33, 37, 39, 41, 45, 52, 54, 56, 57, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 37, 41, 44, 46, 49, 50, 51, 56, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 30, 37, 41, 44, 50, 51, 52, 56, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 30, 34, 37, 39, 44, 45, 50, 52, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 29, 30, 37, 41, 49, 52, 56, 58, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 28, 37, 41, 45, 46, 49, 50, 56, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 28, 34, 37, 39, 46, 49, 50, 51, 56, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 28, 34, 37, 39, 44, 45, 46, 50, 51, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 25, 27, 28, 29, 30, 34, 37, 39, 45, 52, 56, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 25, 30, 33, 35, 37, 41, 49, 52, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 25, 28, 30, 33, 34, 35, 37, 39, 45, 52, 56, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 32, 34, 37, 40, 41, 49, 52, 55, 56, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 28, 32, 34, 37, 39, 40, 45, 52, 53, 56, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 25, 30, 34, 37, 40, 41, 44, 51, 52, 55, 56, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 25, 30, 34, 37, 39, 40, 44, 45, 52, 53, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 25, 28, 37, 39, 40, 41, 45, 46, 56, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 25, 30, 37, 41, 49, 52, 53, 55, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 25, 28, 30, 34, 37, 39, 45, 52, 53, 55, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 25, 34, 37, 39, 40, 41, 46, 49, 56, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 20, 26, 34, 40, 41, 42, 43, 47, 53, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 20, 23, 26, 34, 40, 41, 42, 44, 47, 49, 53, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 20, 26, 35, 39, 41, 42, 43, 47, 54, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 20, 23, 26, 35, 39, 41, 42, 44, 47, 49, 54, 61, 63 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 353
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS179[3], DS179[4], DS179[5], DS179[7], DS179[9], DS179[13], DS179[14], DS179[15], DS179[17], DS179[18], DS179[19], DS179[20], DS179[21], DS179[22], DS179[23], DS179[24], DS179[25], DS179[26], DS179[27], DS179[28], DS179[29], DS179[33], DS179[34], DS179[35], DS179[36], DS179[37], DS179[38], DS179[39], DS179[40], DS179[41], DS179[42], DS179[43], DS179[44], DS179[45], DS179[46], DS179[48], DS179[50], DS179[51], DS179[52], DS179[54], DS179[55], DS179[56], DS179[57], DS179[58], DS179[59], DS179[60], DS179[61], DS179[62], DS179[63], DS179[64], DS179[65], DS179[66], DS179[67], DS179[68], DS179[69], DS179[70], DS179[71], DS179[72], DS179[73], DS179[74], DS179[75], DS179[76], DS179[77], DS179[78], DS179[79], DS179[80], DS179[81], DS179[82], DS179[83], DS179[84], DS179[85], DS179[86], DS179[87], DS179[88], DS179[89], DS179[90], DS179[91], DS179[92], DS179[93], DS179[94], DS179[95], DS179[96], DS179[97], DS179[98], DS179[99], DS179[100], DS179[101], DS179[102], DS179[103], DS179[104], DS179[105], DS179[106], DS179[108], DS179[109], DS179[110], DS179[111], DS179[112], DS179[113], DS179[114], DS179[115], DS179[116], DS179[118], DS179[120], DS179[121], DS179[122], DS179[123], DS179[125], DS179[126], DS179[127], DS179[128], DS179[129], DS179[130], DS179[131], DS179[132], DS179[133], DS179[134], DS179[135], DS179[136], DS179[137], DS179[138], DS179[139], DS179[140], DS179[141], DS179[142], DS179[144], DS179[145], DS179[146], DS179[147], DS179[148], DS179[149], DS179[150], DS179[151], DS179[152], DS179[153], DS179[155], DS179[156], DS179[157], DS179[158], DS179[159], DS179[160], DS179[161], DS179[162], DS179[163], DS179[164], DS179[165], DS179[166], DS179[167], DS179[168], DS179[169], DS179[170], DS179[171], DS179[172], DS179[173], DS179[174], DS179[175], DS179[176], DS179[177], DS179[178], DS179[179], DS179[180], DS179[181], DS179[182], DS179[183], DS179[184], DS179[185], DS179[186], DS179[187], DS179[188], DS179[189], DS179[190], DS179[191], DS179[192], DS179[193], DS179[194], DS179[196], DS179[199], DS179[200], DS179[202], DS179[203], DS179[204], DS179[205], DS179[206], DS179[207], DS179[208], DS179[209], DS179[210], DS179[211], DS179[212], DS179[213], DS179[214], DS179[215], DS179[216], DS179[217], DS179[218], DS179[220], DS179[221], DS179[222], DS179[223], DS179[224], DS179[225], DS179[226], DS179[227], DS179[228], DS179[229], DS179[230], DS179[231], DS179[232], DS179[233], DS179[234], DS179[235], DS179[236], DS179[237], DS179[238], DS179[240], DS179[241], DS179[242], DS179[243], DS179[244], DS179[245], DS179[246], DS179[247], DS179[248], DS179[249], DS179[252], DS179[253], DS179[254], DS179[255], DS179[257], DS179[258], DS179[259], DS179[260], DS179[261], DS179[262], DS179[263], DS179[264], DS179[265], DS179[266], DS179[267], DS179[268], DS179[269], DS179[270], DS179[271], DS179[272], DS179[273], DS179[274], DS179[275], DS179[276], DS179[277], DS179[278], DS179[279], DS179[280], DS179[281], DS179[282], DS179[283], DS179[284], DS179[285], DS179[286], DS179[287], DS179[288], DS179[289], DS179[290], DS179[291], DS179[292], DS179[293], DS179[294], DS179[295], DS179[296], DS179[297], DS179[298], DS179[299], DS179[300], DS179[301], DS179[302], DS179[303], DS179[304], DS179[306], DS179[308], DS179[310], DS179[311], DS179[313], DS179[314], DS179[316], DS179[317], DS179[318], DS179[319], DS179[320], DS179[321], DS179[322], DS179[323], DS179[324], DS179[325], DS179[326], DS179[328], DS179[329], DS179[330], DS179[331], DS179[332], DS179[333], DS179[334], DS179[335], DS179[336], DS179[337], DS179[338], DS179[339], DS179[340], DS179[341], DS179[342], DS179[343], DS179[344], DS179[345], DS179[346], DS179[347], DS179[348], DS179[349], DS179[350], DS179[351], DS179[352], DS179[353], DS179[354], DS179[355], DS179[356], DS179[357], DS179[358], DS179[359], DS179[360], DS179[361], DS179[362], DS179[363], DS179[364], DS179[365], DS179[366], DS179[367], DS179[368], DS179[369], DS179[370], DS179[371], DS179[372], DS179[373], DS179[374], DS179[375], DS179[376], DS179[377], DS179[378], DS179[379], DS179[380], DS179[381], DS179[382], DS179[383], DS179[384], DS179[385], DS179[386], DS179[387], DS179[388]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,179].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,179] is 22
### The list of all inequivalent reversible (64,28,12) DSs in group [64,179] is 
  
  
RDS179:=[ [ 2, 4, 6, 8, 9, 10, 11, 13, 18, 19, 20, 22, 24, 28, 30, 35, 41, 42, 43, 45, 48, 50, 53, 58, 60, 61, 62, 63 ], [ 2, 4, 6, 8, 9, 10, 11, 13, 18, 19, 20, 22, 23, 24, 28, 30, 35, 41, 42, 44, 48, 50, 53, 59, 61, 62, 63, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 18, 19, 21, 22, 23, 24, 26, 30, 33, 41, 47, 49, 50, 51, 55, 58, 59, 60, 63 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 18, 19, 21, 22, 23, 24, 26, 28, 30, 33, 41, 44, 47, 50, 55, 59, 62, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 11, 13, 14, 16, 18, 19, 24, 28, 30, 35, 37, 41, 43, 45, 48, 50, 53, 58, 60, 61, 62, 63 ], [ 2, 3, 4, 8, 9, 10, 11, 13, 14, 16, 18, 19, 23, 24, 28, 30, 35, 37, 41, 44, 48, 50, 53, 59, 61, 62, 63, 64 ], [ 2, 3, 4, 7, 8, 9, 10, 11, 13, 14, 18, 19, 21, 23, 24, 28, 30, 32, 35, 41, 44, 50, 52, 53, 59, 62, 63, 64 ], [ 2, 3, 4, 6, 7, 8, 9, 10, 13, 14, 18, 19, 20, 21, 22, 23, 24, 28, 35, 41, 42, 44, 50, 53, 59, 62, 63, 64 ], [ 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 24, 30, 35, 37, 41, 44, 48, 50, 53, 56, 61, 63, 64 ], [ 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 18, 19, 21, 22, 23, 28, 30, 33, 37, 41, 44, 50, 55, 59, 62, 63, 64 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 14, 16, 18, 19, 21, 22, 23, 24, 28, 30, 37, 41, 44, 48, 50, 59, 61, 62, 64 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 16, 18, 19, 21, 22, 24, 28, 30, 34, 37, 41, 48, 50, 54, 61, 62, 63 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 17, 22, 23, 24, 26, 30, 35, 41, 47, 49, 50, 51, 53, 57, 58, 59, 60, 63 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 17, 22, 23, 24, 26, 28, 30, 35, 41, 44, 47, 50, 53, 57, 59, 62, 63, 64 ], [ 1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 18, 19, 21, 24, 28, 30, 35, 41, 43, 45, 48, 50, 53, 58, 60, 61, 62, 63 ], [ 1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 18, 19, 21, 23, 24, 28, 30, 35, 41, 44, 48, 50, 53, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 16, 18, 19, 20, 23, 24, 28, 30, 37, 41, 42, 44, 48, 50, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 17, 22, 23, 28, 30, 35, 37, 41, 44, 50, 53, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 24, 28, 30, 35, 37, 39, 40, 41, 48, 50, 53, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 13, 14, 15, 18, 19, 23, 26, 28, 35, 36, 38, 41, 44, 47, 50, 53, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 18, 19, 23, 28, 30, 31, 35, 41, 44, 48, 50, 53, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 18, 19, 20, 22, 23, 26, 28, 35, 41, 42, 44, 47, 50, 53, 59, 62, 63, 64 ] ];
  
  
  
   
   
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