### 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 [64,111]. 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 [64,111].
    
    
# 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(64,111));' can be 
# used to create a list e of the elements of the group [64,111].
# In our list of (64,28,12) DSs in group [64,111], we have [1, 
# 2, 3, 4, 5, 6, 8, 12, 13, 15, 16, 18, 20, 23, 24, 
# 25, 27, 35, 36, 38, 40, 44, 50, 56, 57, 58, 59, 61].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[6], e[8], e[12], e[13], e[15], e[16], e[18], e[20], e[23], e[24], e[25], 
# e[27], e[35], e[36], e[38], e[40], e[44], e[50], e[56], e[57], e[58], e[59], e[61]]
# where e is the list of the elements of the group [64,111] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,111));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 111]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,111] is 616
### The list of all inequivalent (64,28,12) DSs in group [64,111] is 
  
  
DS111:=[ [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 15, 16, 18, 20, 23, 24, 25, 27, 35, 36, 38, 40, 44, 50, 56, 57, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 16, 20, 23, 25, 27, 29, 34, 39, 40, 41, 43, 47, 49, 50, 55, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 16, 20, 23, 24, 27, 29, 34, 39, 40, 41, 44, 48, 49, 50, 55, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 16, 18, 20, 25, 27, 29, 34, 40, 45, 46, 47, 49, 50, 55, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 16, 18, 20, 23, 24, 25, 27, 29, 34, 40, 44, 49, 50, 55, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 16, 20, 23, 25, 27, 29, 30, 38, 39, 40, 41, 43, 47, 50, 52, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 16, 20, 23, 24, 27, 29, 30, 38, 39, 40, 41, 44, 48, 50, 52, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 16, 17, 20, 23, 26, 27, 28, 30, 31, 33, 41, 44, 45, 54, 57, 58, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 20, 26, 27, 28, 30, 31, 38, 41, 44, 46, 57, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 20, 23, 26, 27, 28, 30, 31, 38, 41, 43, 45, 46, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 16, 17, 20, 26, 27, 28, 30, 31, 34, 35, 41, 43, 53, 55, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 17, 26, 27, 28, 30, 31, 35, 36, 38, 39, 41, 42, 43, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 17, 26, 27, 28, 30, 31, 33, 35, 38, 39, 41, 42, 46, 54, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 17, 20, 26, 27, 28, 30, 31, 35, 36, 38, 41, 43, 56, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 17, 20, 26, 27, 28, 30, 31, 33, 35, 38, 41, 46, 54, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 26, 27, 28, 30, 31, 35, 36, 37, 39, 41, 42, 44, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 26, 27, 28, 30, 31, 34, 35, 37, 39, 41, 42, 46, 55, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 20, 26, 27, 28, 30, 31, 35, 36, 37, 41, 44, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 20, 26, 27, 28, 30, 31, 34, 35, 37, 41, 46, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 17, 26, 29, 30, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 52, 53, 55, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 29, 30, 32, 33, 39, 40, 41, 45, 46, 47, 48, 52, 54, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 24, 25, 29, 30, 32, 33, 39, 40, 41, 43, 44, 45, 46, 52, 54, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 23, 25, 29, 30, 32, 33, 39, 40, 41, 43, 47, 52, 54, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 23, 24, 29, 30, 32, 33, 39, 40, 41, 44, 48, 52, 54, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 18, 23, 24, 29, 30, 32, 33, 39, 40, 42, 48, 52, 54, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 20, 29, 32, 37, 39, 40, 41, 45, 46, 47, 48, 49, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 20, 24, 25, 29, 32, 37, 39, 40, 41, 43, 44, 45, 46, 49, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 20, 23, 25, 29, 32, 37, 39, 40, 41, 43, 47, 49, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 20, 23, 24, 29, 32, 37, 39, 40, 41, 44, 48, 49, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 18, 29, 32, 37, 39, 40, 42, 44, 45, 46, 47, 48, 49, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 18, 23, 24, 29, 32, 37, 39, 40, 42, 48, 49, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 18, 20, 25, 29, 32, 37, 40, 45, 46, 47, 49, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 17, 23, 25, 29, 32, 37, 39, 41, 42, 43, 44, 46, 47, 49, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17, 24, 26, 29, 32, 34, 35, 36, 39, 41, 42, 47, 49, 53, 54, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17, 24, 26, 29, 32, 33, 35, 36, 39, 41, 42, 47, 49, 53, 55, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 18, 20, 24, 26, 29, 32, 34, 37, 38, 40, 47, 49, 53, 54, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 17, 26, 29, 30, 32, 34, 36, 37, 38, 39, 41, 42, 43, 52, 54, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 17, 24, 26, 29, 32, 33, 36, 37, 38, 39, 41, 42, 47, 49, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 24, 26, 29, 32, 34, 36, 38, 40, 41, 42, 47, 49, 53, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 18, 20, 24, 26, 29, 32, 33, 34, 36, 38, 40, 47, 49, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 17, 20, 24, 26, 29, 32, 33, 34, 36, 38, 41, 47, 49, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 17, 26, 29, 30, 32, 34, 36, 39, 41, 42, 43, 52, 54, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 17, 24, 26, 29, 32, 34, 36, 39, 41, 42, 47, 49, 54, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 17, 24, 26, 29, 32, 33, 36, 39, 41, 42, 47, 49, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 20, 28, 29, 31, 36, 39, 40, 41, 45, 46, 47, 48, 51, 56, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 20, 24, 25, 28, 29, 31, 36, 39, 40, 41, 43, 44, 45, 46, 51, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 20, 23, 25, 29, 30, 31, 34, 39, 40, 41, 43, 47, 52, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 20, 23, 25, 28, 29, 31, 36, 39, 40, 41, 43, 47, 51, 56, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 20, 23, 24, 29, 30, 31, 34, 39, 40, 41, 44, 48, 52, 55, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 20, 23, 24, 28, 29, 31, 36, 39, 40, 41, 44, 48, 51, 56, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 23, 24, 25, 29, 30, 31, 34, 40, 44, 52, 55, 57, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 23, 24, 25, 28, 29, 31, 36, 40, 44, 51, 56, 57, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 20, 23, 25, 29, 31, 38, 39, 40, 41, 43, 47, 49, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 20, 23, 24, 29, 31, 38, 39, 40, 41, 44, 48, 49, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 29, 31, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 23, 24, 29, 31, 38, 39, 40, 42, 48, 49, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 25, 29, 31, 38, 40, 45, 46, 47, 49, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 25, 29, 31, 38, 40, 44, 49, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 23, 25, 29, 31, 38, 39, 41, 42, 43, 44, 46, 47, 49, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 17, 26, 29, 30, 31, 33, 35, 36, 39, 41, 42, 44, 52, 53, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 26, 29, 30, 31, 34, 37, 38, 40, 44, 52, 53, 54, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 17, 26, 29, 30, 31, 34, 36, 37, 38, 39, 41, 42, 44, 52, 54, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 17, 26, 28, 29, 31, 33, 36, 37, 38, 39, 41, 42, 46, 51, 55, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 17, 25, 26, 29, 31, 33, 36, 37, 38, 39, 41, 42, 48, 49, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 26, 29, 30, 31, 33, 36, 37, 40, 41, 42, 44, 52, 53, 55, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 26, 28, 29, 31, 33, 36, 37, 40, 41, 42, 46, 51, 53, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 26, 29, 30, 31, 34, 36, 38, 40, 41, 42, 44, 52, 53, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 26, 28, 29, 31, 34, 36, 38, 40, 41, 42, 46, 51, 53, 54, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 25, 26, 29, 31, 34, 36, 38, 40, 41, 42, 48, 49, 53, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 21, 27, 29, 30, 34, 35, 38, 39, 41, 46, 47, 48, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 29, 30, 31, 33, 34, 36, 38, 40, 44, 52, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 28, 29, 31, 33, 34, 36, 38, 40, 46, 51, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 25, 26, 29, 31, 33, 34, 36, 38, 40, 48, 49, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 20, 26, 29, 30, 31, 33, 34, 36, 38, 41, 44, 52, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 19, 20, 28, 30, 33, 41, 46, 47, 48, 49, 54, 55, 56, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 26, 29, 30, 31, 34, 36, 39, 41, 42, 44, 52, 54, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 26, 29, 30, 31, 33, 36, 39, 41, 42, 44, 52, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 26, 28, 29, 31, 34, 36, 39, 41, 42, 46, 51, 54, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 26, 28, 29, 31, 33, 36, 39, 41, 42, 46, 51, 55, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 25, 26, 29, 31, 34, 36, 39, 41, 42, 48, 49, 54, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 25, 26, 29, 31, 33, 36, 39, 41, 42, 48, 49, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 25, 26, 28, 36, 39, 41, 42, 44, 48, 49, 50, 52, 56, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 24, 26, 28, 36, 39, 41, 42, 43, 47, 49, 50, 52, 56, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 23, 26, 28, 34, 39, 41, 42, 43, 45, 49, 50, 52, 55, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 23, 26, 28, 33, 39, 41, 42, 44, 45, 49, 50, 52, 54, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 23, 25, 26, 28, 36, 39, 41, 42, 43, 45, 48, 49, 50, 52, 56, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 23, 25, 26, 28, 33, 39, 41, 42, 45, 46, 48, 49, 50, 52, 54, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 23, 24, 26, 28, 36, 39, 41, 42, 44, 45, 47, 49, 50, 52, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 23, 24, 26, 28, 34, 39, 41, 42, 45, 46, 47, 49, 50, 52, 55, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 20, 25, 26, 28, 34, 41, 46, 48, 49, 50, 52, 55, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 20, 24, 26, 28, 36, 41, 43, 47, 49, 50, 52, 56, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 20, 24, 26, 28, 33, 41, 46, 47, 49, 50, 52, 54, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16, 17, 20, 24, 25, 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12, 16, 18, 27, 34, 36, 37, 38, 39, 41, 45, 49, 50, 54, 56, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 18, 25, 27, 30, 31, 34, 35, 36, 39, 41, 53, 54, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 28, 34, 36, 37, 38, 39, 40, 45, 49, 51, 54, 56, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 18, 23, 25, 27, 36, 38, 41, 45, 46, 47, 50, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 23, 25, 28, 36, 38, 40, 45, 46, 47, 51, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 20, 28, 33, 35, 38, 42, 43, 46, 51, 54, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 20, 27, 29, 33, 34, 38, 39, 42, 46, 51, 53, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 27, 30, 38, 45, 46, 49, 51, 52, 53, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 30, 33, 35, 38, 41, 43, 46, 52, 54, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 27, 35, 36, 38, 41, 43, 46, 50, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 28, 35, 36, 38, 40, 43, 46, 51, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 19, 30, 33, 36, 38, 41, 43, 44, 46, 49, 52, 54, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 25, 27, 35, 36, 38, 41, 46, 47, 50, 53, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 25, 28, 35, 36, 38, 40, 46, 47, 51, 53, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 19, 30, 34, 36, 37, 41, 43, 44, 46, 49, 52, 55, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 20, 28, 33, 38, 42, 44, 46, 51, 53, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 20, 27, 34, 38, 42, 44, 46, 50, 53, 55, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 30, 33, 38, 41, 44, 46, 52, 53, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 27, 36, 38, 41, 44, 46, 50, 53, 56, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 30, 34, 38, 40, 44, 46, 52, 53, 55, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 28, 36, 38, 40, 44, 46, 51, 53, 56, 57, 59, 62 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 458
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS111[5], DS111[6], DS111[8], DS111[11], DS111[14], DS111[17], DS111[20], DS111[23], DS111[26], DS111[28], DS111[36], DS111[39], DS111[40], DS111[42], DS111[61], DS111[66], DS111[67], DS111[69], DS111[70], DS111[75], DS111[79], DS111[80], DS111[83], DS111[85], DS111[89], DS111[93], DS111[99], DS111[102], DS111[103], DS111[107], DS111[108], DS111[110], DS111[112], DS111[113], DS111[114], DS111[117], DS111[123], DS111[124], DS111[126], DS111[133], DS111[135], DS111[137], DS111[141], DS111[145], DS111[146], DS111[148], DS111[150], DS111[154], DS111[155], DS111[156], DS111[157], DS111[158], DS111[163], DS111[165], DS111[166], DS111[169], DS111[171], DS111[175], DS111[178], DS111[179], DS111[180], DS111[181], DS111[182], DS111[183], DS111[184], DS111[185], DS111[186], DS111[187], DS111[188], DS111[189], DS111[190], DS111[191], DS111[192], DS111[193], DS111[194], DS111[195], DS111[196], DS111[197], DS111[198], DS111[199], DS111[200], DS111[201], DS111[202], DS111[203], DS111[204], DS111[205], DS111[206], DS111[207], DS111[208], DS111[209], DS111[210], DS111[211], DS111[212], DS111[213], DS111[214], DS111[215], DS111[216], DS111[217], DS111[218], DS111[219], DS111[220], DS111[221], DS111[222], DS111[223], DS111[224], DS111[225], DS111[226], DS111[227], DS111[228], DS111[229], DS111[230], DS111[231], DS111[232], DS111[233], DS111[234], DS111[235], DS111[236], DS111[237], DS111[238], DS111[239], DS111[240], DS111[241], DS111[243], DS111[244], DS111[245], DS111[247], DS111[248], DS111[249], DS111[250], DS111[251], DS111[252], DS111[253], DS111[254], DS111[255], DS111[256], DS111[257], DS111[258], DS111[259], DS111[260], DS111[261], DS111[262], DS111[263], DS111[264], DS111[265], DS111[266], DS111[267], DS111[268], DS111[269], DS111[270], DS111[271], DS111[273], DS111[274], DS111[275], DS111[276], DS111[277], DS111[278], DS111[279], DS111[280], DS111[281], DS111[284], DS111[285], DS111[286], DS111[287], DS111[288], DS111[289], DS111[290], DS111[291], DS111[292], DS111[293], DS111[294], DS111[295], DS111[296], DS111[297], DS111[298], DS111[299], DS111[300], DS111[301], DS111[302], DS111[303], DS111[304], DS111[305], DS111[306], DS111[307], DS111[308], DS111[309], DS111[310], DS111[314], DS111[315], DS111[316], DS111[317], DS111[318], DS111[319], DS111[320], DS111[321], DS111[324], DS111[325], DS111[326], DS111[328], DS111[329], DS111[330], DS111[331], DS111[332], DS111[333], DS111[334], DS111[335], DS111[336], DS111[337], DS111[338], DS111[339], DS111[340], DS111[341], DS111[342], DS111[343], DS111[344], DS111[345], DS111[346], DS111[347], DS111[348], DS111[349], DS111[350], DS111[352], DS111[353], DS111[355], DS111[357], DS111[358], DS111[359], DS111[360], DS111[361], DS111[362], DS111[363], DS111[364], DS111[365], DS111[366], DS111[367], DS111[368], DS111[369], DS111[370], DS111[371], DS111[372], DS111[373], DS111[374], DS111[375], DS111[376], DS111[377], DS111[378], DS111[379], DS111[380], DS111[381], DS111[382], DS111[383], DS111[384], DS111[385], DS111[386], DS111[387], DS111[388], DS111[389], DS111[390], DS111[391], DS111[392], DS111[393], DS111[394], DS111[395], DS111[396], DS111[397], DS111[398], DS111[399], DS111[401], DS111[402], DS111[403], DS111[404], DS111[405], DS111[406], DS111[407], DS111[408], DS111[409], DS111[410], DS111[411], DS111[412], DS111[413], DS111[414], DS111[415], DS111[416], DS111[417], DS111[418], DS111[419], DS111[420], DS111[421], DS111[422], DS111[423], DS111[424], DS111[425], DS111[426], DS111[427], DS111[429], DS111[430], DS111[431], DS111[432], DS111[433], DS111[434], DS111[435], DS111[436], DS111[437], DS111[438], DS111[439], DS111[440], DS111[441], DS111[442], DS111[443], DS111[444], DS111[445], DS111[446], DS111[447], DS111[448], DS111[449], DS111[450], DS111[451], DS111[452], DS111[453], DS111[454], DS111[455], DS111[456], DS111[457], DS111[458], DS111[459], DS111[460], DS111[461], DS111[462], DS111[463], DS111[464], DS111[465], DS111[466], DS111[467], DS111[468], DS111[469], DS111[470], DS111[472], DS111[473], DS111[474], DS111[475], DS111[476], DS111[477], DS111[478], DS111[483], DS111[484], DS111[487], DS111[488], DS111[489], DS111[492], DS111[493], DS111[494], DS111[495], DS111[496], DS111[497], DS111[498], DS111[499], DS111[500], DS111[502], DS111[503], DS111[504], DS111[505], DS111[506], DS111[508], DS111[509], DS111[510], DS111[511], DS111[512], DS111[513], DS111[514], DS111[515], DS111[516], DS111[517], DS111[518], DS111[519], DS111[520], DS111[521], DS111[522], DS111[524], DS111[525], DS111[526], DS111[527], DS111[528], DS111[529], DS111[530], DS111[531], DS111[532], DS111[533], DS111[536], DS111[537], DS111[538], DS111[539], DS111[540], DS111[541], DS111[543], DS111[544], DS111[545], DS111[546], DS111[548], DS111[549], DS111[550], DS111[551], DS111[552], DS111[553], DS111[554], DS111[555], DS111[556], DS111[557], DS111[558], DS111[559], DS111[560], DS111[561], DS111[562], DS111[566], DS111[567], DS111[568], DS111[569], DS111[570], DS111[571], DS111[572], DS111[573], DS111[574], DS111[575], DS111[577], DS111[579], DS111[580], DS111[581], DS111[582], DS111[583], DS111[584], DS111[585], DS111[586], DS111[587], DS111[590], DS111[591], DS111[592], DS111[593], DS111[594], DS111[595], DS111[596], DS111[597], DS111[598], DS111[599], DS111[600], DS111[601], DS111[602], DS111[603], DS111[604], DS111[605], DS111[606], DS111[607], DS111[608], DS111[609], DS111[610], DS111[611], DS111[612], DS111[613], DS111[614], DS111[615], DS111[616]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,111].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,111] is 16
### The list of all inequivalent reversible (64,28,12) DSs in group [64,111] is 
  
  
RDS111:=[ [ 2, 3, 6, 8, 9, 13, 15, 17, 18, 20, 22, 25, 26, 27, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 48, 51, 62, 63 ], [ 2, 3, 6, 8, 9, 10, 15, 17, 18, 20, 22, 25, 26, 32, 35, 36, 37, 40, 41, 42, 48, 49, 50, 51, 52, 53, 54, 55 ], [ 2, 3, 4, 6, 8, 9, 13, 15, 19, 20, 22, 25, 26, 27, 30, 31, 32, 33, 34, 36, 37, 39, 42, 48, 51, 57, 62, 63 ], [ 2, 3, 4, 6, 8, 9, 10, 15, 19, 20, 22, 25, 26, 32, 35, 36, 37, 39, 42, 48, 49, 50, 51, 52, 53, 54, 55, 57 ], [ 2, 3, 4, 5, 6, 8, 11, 12, 13, 15, 17, 19, 21, 22, 25, 32, 33, 34, 36, 37, 40, 43, 44, 45, 47, 61, 63, 64 ], [ 2, 3, 4, 5, 6, 8, 11, 12, 13, 15, 17, 19, 21, 22, 24, 25, 32, 33, 34, 36, 37, 40, 44, 45, 46, 58, 59, 63 ], [ 2, 3, 4, 5, 6, 8, 9, 13, 15, 17, 19, 21, 22, 25, 26, 27, 30, 31, 32, 33, 34, 36, 37, 40, 48, 51, 62, 63 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 15, 17, 19, 21, 22, 25, 26, 32, 35, 36, 37, 40, 48, 49, 50, 51, 52, 53, 54, 55 ], [ 1, 2, 3, 5, 7, 8, 9, 13, 15, 17, 18, 21, 25, 26, 27, 30, 31, 32, 33, 34, 36, 37, 40, 41, 48, 51, 62, 63 ], [ 1, 2, 3, 5, 7, 8, 9, 10, 15, 17, 18, 21, 25, 26, 32, 35, 36, 37, 40, 41, 48, 49, 50, 51, 52, 53, 54, 55 ], [ 1, 2, 3, 4, 7, 8, 11, 12, 13, 15, 17, 19, 20, 25, 32, 33, 34, 36, 37, 40, 42, 43, 44, 45, 47, 61, 63, 64 ], [ 1, 2, 3, 4, 7, 8, 11, 12, 13, 15, 17, 19, 20, 24, 25, 32, 33, 34, 36, 37, 40, 42, 44, 45, 46, 58, 59, 63 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 15, 17, 19, 20, 25, 26, 27, 30, 31, 32, 33, 34, 36, 37, 40, 42, 48, 51, 62, 63 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 15, 17, 19, 20, 25, 26, 32, 35, 36, 37, 40, 42, 48, 49, 50, 51, 52, 53, 54, 55 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 13, 15, 19, 21, 25, 26, 27, 30, 31, 32, 33, 34, 36, 37, 39, 48, 51, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 15, 19, 21, 25, 26, 32, 35, 36, 37, 39, 48, 49, 50, 51, 52, 53, 54, 55, 57 ] ];
  
  
  
   
   
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