### 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 [64,129]. 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 [64,129].
    
    
# 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(64,129));' can be 
# used to create a list e of the elements of the group [64,129].
# In our list of (64,28,12) DSs in group [64,129], we have [1, 
# 2, 3, 4, 5, 6, 9, 12, 14, 15, 17, 19, 20, 23, 24, 
# 27, 30, 36, 40, 46, 47, 51, 52, 58, 59, 60, 61, 62].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[6], e[9], e[12], e[14], e[15], e[17], e[19], e[20], e[23], e[24], e[27], 
# e[30], e[36], e[40], e[46], e[47], e[51], e[52], e[58], e[59], e[60], e[61], e[62]]
# where e is the list of the elements of the group [64,129] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,129));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 129]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,129] is 1466
### The list of all inequivalent (64,28,12) DSs in group [64,129] is 
  
  
DS129:=[ [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 17, 19, 20, 23, 24, 27, 30, 36, 40, 46, 47, 51, 52, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 17, 19, 20, 23, 24, 27, 30, 36, 40, 43, 46, 47, 51, 52, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 20, 23, 24, 29, 32, 36, 39, 40, 41, 43, 45, 46, 47, 49, 52, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 20, 23, 24, 27, 29, 32, 36, 39, 40, 41, 45, 46, 47, 50, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 19, 20, 23, 24, 32, 36, 39, 43, 45, 46, 47, 49, 50, 51, 52, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 19, 20, 23, 24, 27, 29, 32, 36, 39, 46, 47, 50, 52, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 19, 20, 23, 24, 27, 29, 32, 36, 39, 43, 46, 47, 50, 52, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 17, 20, 23, 24, 29, 32, 36, 41, 43, 45, 46, 47, 49, 52, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 17, 20, 23, 24, 27, 29, 32, 36, 41, 45, 46, 47, 50, 52, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 17, 19, 20, 23, 24, 32, 36, 40, 45, 46, 47, 49, 50, 51, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 17, 19, 20, 23, 24, 29, 32, 36, 40, 46, 47, 49, 52, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, 17, 19, 20, 23, 24, 29, 32, 36, 40, 43, 46, 47, 49, 52, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15, 20, 29, 32, 33, 35, 36, 39, 40, 41, 43, 49, 52, 54, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15, 20, 27, 29, 32, 35, 36, 39, 40, 41, 43, 50, 52, 53, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15, 19, 20, 32, 33, 35, 36, 39, 43, 49, 50, 51, 52, 54, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15, 17, 20, 29, 32, 33, 35, 36, 41, 43, 49, 52, 54, 57, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15, 17, 20, 27, 29, 32, 35, 36, 41, 43, 50, 52, 53, 57, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15, 17, 19, 20, 32, 35, 36, 40, 43, 49, 50, 51, 52, 53, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 14, 15, 19, 20, 23, 24, 27, 31, 36, 39, 46, 47, 51, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 14, 15, 19, 20, 23, 24, 27, 31, 36, 39, 43, 46, 47, 51, 57, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 20, 24, 29, 31, 34, 38, 39, 40, 41, 46, 47, 49, 54, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 20, 24, 29, 31, 33, 34, 38, 39, 40, 41, 46, 47, 49, 53, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 17, 20, 24, 29, 31, 34, 38, 41, 46, 47, 49, 54, 56, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 17, 20, 24, 29, 31, 33, 34, 38, 41, 46, 47, 49, 53, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 15, 20, 29, 31, 36, 39, 40, 41, 43, 49, 53, 54, 55, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 15, 20, 29, 31, 33, 36, 39, 40, 41, 43, 49, 55, 58, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 15, 17, 20, 29, 31, 36, 41, 43, 49, 53, 54, 55, 57, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 15, 17, 20, 29, 31, 33, 36, 41, 43, 49, 55, 57, 58, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 20, 24, 26, 30, 38, 40, 43, 47, 52, 53, 54, 55, 56, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 16, 18, 20, 24, 30, 33, 37, 40, 43, 48, 52, 55, 57, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 18, 20, 21, 26, 29, 33, 36, 37, 38, 42, 44, 46, 51, 55, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 18, 20, 21, 24, 26, 29, 33, 36, 37, 38, 42, 43, 44, 47, 51, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 18, 20, 21, 23, 26, 29, 33, 36, 37, 38, 42, 43, 45, 46, 51, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 18, 20, 21, 23, 24, 26, 29, 33, 36, 37, 38, 42, 45, 47, 51, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 18, 20, 21, 29, 33, 36, 42, 44, 46, 47, 48, 51, 55, 56, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 18, 20, 21, 29, 33, 35, 36, 42, 44, 45, 46, 47, 48, 51, 54, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 18, 20, 21, 24, 29, 33, 35, 36, 42, 43, 44, 45, 48, 51, 54, 56, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 18, 20, 21, 23, 29, 33, 36, 42, 43, 45, 46, 47, 48, 51, 55, 56, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 18, 20, 21, 23, 29, 33, 35, 36, 42, 43, 46, 47, 48, 51, 54, 56, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 18, 20, 21, 23, 24, 29, 33, 36, 42, 43, 45, 48, 51, 55, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 18, 20, 21, 23, 24, 29, 33, 35, 36, 42, 48, 51, 54, 56, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 24, 26, 29, 36, 37, 38, 39, 40, 42, 43, 44, 47, 51, 55, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 23, 24, 26, 29, 36, 37, 38, 39, 40, 42, 45, 47, 51, 55, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 20, 21, 26, 29, 38, 42, 44, 46, 51, 53, 54, 55, 56, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 20, 21, 26, 29, 33, 35, 38, 42, 43, 44, 45, 46, 51, 54, 56, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 20, 21, 24, 26, 29, 38, 42, 43, 44, 47, 51, 53, 54, 55, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 20, 21, 23, 26, 29, 38, 42, 43, 45, 46, 51, 53, 54, 55, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 20, 21, 23, 26, 29, 33, 35, 38, 42, 46, 51, 54, 56, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 20, 21, 23, 26, 29, 33, 35, 38, 42, 43, 46, 51, 54, 56, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 20, 21, 23, 24, 26, 29, 38, 42, 45, 47, 51, 53, 54, 55, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 21, 24, 29, 35, 36, 37, 39, 43, 44, 45, 48, 51, 56, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 21, 23, 24, 29, 35, 36, 37, 39, 48, 51, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 29, 35, 37, 42, 44, 45, 46, 47, 48, 51, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 29, 33, 37, 42, 43, 44, 46, 47, 48, 51, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 24, 29, 37, 42, 43, 44, 48, 51, 53, 54, 55, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 24, 29, 35, 37, 42, 43, 44, 45, 48, 51, 53, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 23, 29, 37, 42, 45, 46, 47, 48, 51, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 23, 29, 35, 37, 42, 43, 46, 47, 48, 51, 53, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 23, 29, 33, 37, 42, 45, 46, 47, 48, 51, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 23, 24, 29, 37, 42, 45, 48, 51, 53, 54, 55, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 23, 24, 29, 35, 37, 42, 48, 51, 53, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 23, 24, 29, 33, 37, 42, 45, 48, 51, 55, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 18, 20, 26, 32, 33, 36, 37, 38, 40, 44, 46, 55, 57, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 18, 20, 24, 26, 32, 33, 36, 37, 38, 40, 43, 44, 47, 55, 57, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 18, 20, 23, 26, 32, 33, 36, 37, 38, 40, 43, 45, 46, 55, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 18, 20, 23, 24, 26, 32, 33, 36, 37, 38, 40, 45, 47, 55, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 16, 18, 20, 24, 32, 33, 35, 36, 40, 43, 44, 45, 48, 54, 56, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 16, 18, 20, 23, 24, 32, 33, 36, 40, 43, 45, 48, 55, 56, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 16, 18, 20, 23, 24, 32, 33, 35, 36, 40, 48, 54, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 26, 32, 38, 40, 44, 46, 53, 54, 55, 56, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 24, 26, 32, 38, 40, 43, 44, 47, 53, 54, 55, 56, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 23, 26, 32, 38, 40, 43, 45, 46, 53, 54, 55, 56, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 23, 26, 32, 33, 35, 38, 40, 43, 46, 54, 56, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 23, 24, 26, 32, 38, 40, 45, 47, 53, 54, 55, 56, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 18, 20, 24, 32, 35, 37, 40, 43, 44, 45, 48, 53, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 18, 20, 23, 24, 32, 37, 40, 45, 48, 53, 54, 55, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 18, 20, 23, 24, 32, 35, 37, 40, 48, 53, 57, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 18, 20, 23, 24, 32, 33, 37, 40, 45, 48, 55, 57, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 20, 23, 26, 32, 36, 39, 40, 41, 43, 45, 46, 53, 54, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 20, 23, 26, 32, 33, 36, 39, 40, 41, 43, 45, 46, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 20, 23, 24, 26, 32, 36, 39, 40, 41, 45, 47, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 20, 23, 24, 26, 32, 33, 36, 39, 40, 41, 45, 47, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 19, 20, 23, 24, 32, 36, 39, 43, 45, 48, 53, 54, 55, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 19, 20, 23, 24, 32, 33, 36, 39, 43, 45, 48, 55, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 19, 20, 23, 24, 32, 33, 35, 36, 39, 48, 54, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 23, 32, 35, 36, 39, 41, 42, 43, 45, 46, 47, 48, 53, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 23, 32, 33, 35, 36, 39, 41, 42, 45, 46, 47, 48, 54, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 23, 26, 32, 36, 39, 41, 42, 43, 45, 46, 53, 54, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 23, 26, 32, 33, 36, 39, 41, 42, 43, 45, 46, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 23, 26, 32, 33, 35, 36, 39, 41, 42, 43, 46, 54, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 23, 24, 26, 32, 36, 39, 41, 42, 45, 47, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 23, 24, 26, 32, 35, 36, 39, 41, 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22, 23, 24, 25, 27, 43, 46, 49, 51, 52, 53, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 25, 27, 30, 51, 53, 59, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 25, 27, 30, 46, 51, 53, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 25, 27, 30, 43, 51, 53, 58, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 25, 27, 30, 43, 46, 51, 53, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 26, 31, 32, 40, 41, 45, 48, 52, 55, 58, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 25, 30, 31, 32, 40, 41, 43, 44, 47, 48, 49, 55, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 24, 26, 27, 32, 40, 41, 45, 46, 48, 49, 55, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 24, 25, 31, 32, 40, 41, 43, 44, 48, 52, 55, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 24, 25, 27, 32, 40, 41, 44, 47, 48, 49, 55, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 23, 27, 32, 40, 41, 44, 45, 49, 55, 58, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 21, 29, 32, 33, 38, 40, 42, 45, 51, 53, 55, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 29, 32, 37, 38, 39, 40, 45, 51, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 21, 29, 32, 33, 34, 40, 42, 45, 46, 51, 53, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 29, 32, 34, 37, 39, 40, 45, 46, 51, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 20, 21, 29, 32, 33, 34, 45, 51, 53, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 22, 25, 27, 29, 30, 36, 41, 42, 43, 50, 53, 54, 55, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 28, 30, 36, 37, 48, 50, 53, 55, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21, 29, 32, 33, 38, 40, 42, 45, 51, 54, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 22, 25, 29, 30, 33, 35, 38, 41, 42, 43, 49, 54, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 29, 32, 34, 37, 40, 42, 45, 51, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 29, 32, 33, 34, 39, 40, 45, 51, 53, 55, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 25, 29, 30, 37, 41, 42, 43, 49, 53, 54, 55, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 25, 29, 30, 33, 37, 41, 42, 43, 49, 55, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 28, 30, 43, 48, 50, 53, 55, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 25, 30, 49, 50, 51, 53, 55, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 25, 30, 43, 49, 50, 51, 53, 55, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 29, 32, 33, 36, 38, 39, 40, 45, 51, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 20, 29, 33, 34, 39, 42, 47, 50, 51, 54, 56, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 25, 26, 30, 40, 41, 43, 44, 46, 49, 52, 55, 58, 59, 63 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 599
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS129[2], DS129[3], DS129[4], DS129[5], DS129[8], DS129[9], DS129[10], DS129[11], DS129[13], DS129[20], DS129[21], DS129[42], DS129[43], DS129[45], DS129[49], DS129[50], DS129[51], DS129[52], DS129[56], DS129[57], DS129[59], DS129[73], DS129[74], DS129[76], DS129[82], DS129[83], DS129[84], DS129[86], DS129[87], DS129[90], DS129[92], DS129[94], DS129[98], DS129[100], DS129[101], DS129[102], DS129[105], DS129[107], DS129[108], DS129[112], DS129[114], DS129[115], DS129[117], DS129[118], DS129[121], DS129[122], DS129[129], DS129[134], DS129[135], DS129[136], DS129[138], DS129[139], DS129[141], DS129[142], DS129[143], DS129[157], DS129[160], DS129[163], DS129[167], DS129[170], DS129[171], DS129[179], DS129[187], DS129[192], DS129[193], DS129[196], DS129[197], DS129[200], DS129[212], DS129[221], DS129[222], DS129[225], DS129[226], DS129[227], DS129[237], DS129[245], DS129[246], DS129[254], DS129[260], DS129[262], DS129[263], DS129[264], DS129[265], DS129[270], DS129[273], DS129[280], DS129[281], DS129[283], DS129[284], DS129[288], DS129[290], DS129[291], DS129[295], DS129[296], DS129[300], DS129[321], DS129[322], DS129[323], DS129[324], DS129[325], DS129[328], DS129[332], DS129[335], DS129[337], DS129[338], DS129[340], DS129[341], DS129[345], DS129[349], DS129[355], DS129[356], DS129[357], DS129[358], DS129[360], DS129[361], DS129[362], DS129[363], DS129[364], DS129[365], DS129[366], DS129[373], DS129[375], DS129[381], DS129[382], DS129[393], DS129[397], DS129[398], DS129[399], DS129[404], DS129[405], DS129[408], DS129[409], DS129[416], DS129[418], DS129[425], DS129[433], DS129[434], DS129[436], DS129[437], DS129[438], DS129[439], DS129[443], DS129[444], DS129[446], DS129[447], DS129[449], DS129[460], DS129[461], DS129[462], DS129[463], DS129[469], DS129[472], DS129[473], DS129[476], DS129[479], DS129[480], DS129[481], DS129[486], DS129[487], DS129[488], DS129[489], DS129[490], DS129[499], DS129[518], DS129[519], DS129[521], DS129[522], DS129[526], DS129[528], DS129[529], DS129[535], DS129[537], DS129[539], DS129[540], DS129[541], DS129[543], DS129[544], DS129[545], DS129[547], DS129[549], DS129[551], DS129[554], DS129[555], DS129[557], DS129[558], DS129[562], DS129[565], DS129[566], DS129[567], DS129[568], DS129[571], DS129[572], DS129[576], DS129[578], DS129[580], DS129[592], DS129[596], DS129[599], DS129[601], DS129[602], DS129[604], DS129[605], DS129[606], DS129[612], DS129[613], DS129[617], DS129[619], DS129[621], DS129[622], DS129[623], DS129[627], DS129[629], DS129[630], DS129[632], DS129[635], DS129[639], DS129[640], DS129[641], DS129[644], DS129[645], DS129[651], DS129[656], DS129[657], DS129[658], DS129[660], DS129[661], DS129[662], DS129[663], DS129[667], DS129[668], DS129[671], DS129[672], DS129[673], DS129[681], DS129[684], DS129[685], DS129[686], DS129[687], DS129[688], DS129[690], DS129[691], DS129[692], DS129[693], DS129[696], DS129[697], DS129[700], DS129[702], DS129[703], DS129[704], DS129[705], DS129[708], DS129[719], DS129[721], DS129[722], DS129[725], DS129[727], DS129[731], DS129[733], DS129[736], DS129[737], DS129[738], DS129[739], DS129[743], DS129[744], DS129[745], DS129[746], DS129[747], DS129[748], DS129[749], DS129[751], DS129[752], DS129[757], DS129[760], DS129[761], DS129[764], DS129[765], DS129[767], DS129[768], DS129[769], DS129[770], DS129[771], DS129[772], DS129[775], DS129[779], DS129[780], DS129[782], DS129[784], DS129[789], DS129[790], DS129[791], DS129[793], DS129[794], DS129[796], DS129[797], DS129[800], DS129[803], DS129[804], DS129[805], DS129[808], DS129[809], DS129[811], DS129[815], DS129[816], DS129[817], DS129[820], DS129[824], DS129[825], DS129[827], DS129[830], DS129[831], DS129[833], DS129[835], DS129[836], DS129[838], DS129[839], DS129[840], DS129[841], DS129[842], DS129[845], DS129[846], DS129[849], DS129[852], DS129[853], DS129[855], DS129[858], DS129[862], DS129[863], DS129[864], DS129[866], DS129[869], DS129[870], DS129[871], DS129[874], DS129[875], DS129[880], DS129[882], DS129[883], DS129[885], DS129[886], DS129[887], DS129[889], DS129[891], DS129[897], DS129[898], DS129[899], DS129[900], DS129[901], DS129[905], DS129[906], DS129[907], DS129[908], DS129[911], DS129[913], DS129[918], DS129[923], DS129[924], DS129[926], DS129[927], DS129[930], DS129[931], DS129[945], DS129[947], DS129[948], DS129[950], DS129[952], DS129[953], DS129[954], DS129[957], DS129[961], DS129[962], DS129[963], DS129[964], DS129[965], DS129[966], DS129[968], DS129[969], DS129[976], DS129[979], DS129[980], DS129[982], DS129[983], DS129[984], DS129[987], DS129[994], DS129[995], DS129[998], DS129[1000], DS129[1001], DS129[1006], DS129[1009], DS129[1011], DS129[1012], DS129[1014], DS129[1017], DS129[1028], DS129[1029], DS129[1034], DS129[1035], DS129[1039], DS129[1040], DS129[1041], DS129[1043], DS129[1044], DS129[1047], DS129[1049], DS129[1050], DS129[1051], DS129[1055], DS129[1056], DS129[1058], DS129[1059], DS129[1062], DS129[1065], DS129[1067], DS129[1068], DS129[1077], DS129[1079], DS129[1080], DS129[1081], DS129[1082], DS129[1083], DS129[1084], DS129[1085], DS129[1087], DS129[1088], DS129[1089], DS129[1090], DS129[1092], DS129[1093], DS129[1094], DS129[1095], DS129[1096], DS129[1097], DS129[1098], DS129[1099], DS129[1100], DS129[1101], DS129[1102], DS129[1103], DS129[1104], DS129[1105], DS129[1106], DS129[1107], DS129[1108], DS129[1109], DS129[1110], DS129[1111], DS129[1112], DS129[1113], DS129[1114], DS129[1115], DS129[1116], DS129[1117], DS129[1118], DS129[1119], DS129[1120], DS129[1121], DS129[1122], DS129[1123], DS129[1124], DS129[1125], DS129[1126], DS129[1127], DS129[1128], DS129[1129], DS129[1130], DS129[1143], DS129[1145], DS129[1150], DS129[1151], DS129[1152], DS129[1154], DS129[1156], DS129[1159], DS129[1162], DS129[1163], DS129[1164], DS129[1165], DS129[1166], DS129[1167], DS129[1168], DS129[1193], DS129[1201], DS129[1202], DS129[1203], DS129[1204], DS129[1205], DS129[1206], DS129[1207], DS129[1208], DS129[1209], DS129[1210], DS129[1211], DS129[1212], DS129[1213], DS129[1214], DS129[1238], DS129[1243], DS129[1244], DS129[1250], DS129[1252], DS129[1253], DS129[1256], DS129[1258], DS129[1259], DS129[1260], DS129[1263], DS129[1264], DS129[1266], DS129[1267], DS129[1269], DS129[1271], DS129[1282], DS129[1287], DS129[1288], DS129[1290], DS129[1293], DS129[1295], DS129[1296], DS129[1297], DS129[1298], DS129[1299], DS129[1300], DS129[1301], DS129[1302], DS129[1303], DS129[1304], DS129[1305], DS129[1306], DS129[1307], DS129[1308], DS129[1309], DS129[1310], DS129[1311], DS129[1312], DS129[1313], DS129[1314], DS129[1315], DS129[1316], DS129[1323], DS129[1324], DS129[1329], DS129[1330], DS129[1332], DS129[1334], DS129[1335], DS129[1337], DS129[1341], DS129[1345], DS129[1348], DS129[1354], DS129[1357], DS129[1359], DS129[1360], DS129[1363], DS129[1364], DS129[1366], DS129[1368], DS129[1369], DS129[1389], DS129[1390], DS129[1396], DS129[1402], DS129[1407], DS129[1409], DS129[1412], DS129[1414], DS129[1416], DS129[1421], DS129[1426], DS129[1428], DS129[1433], DS129[1438], DS129[1440], DS129[1442], DS129[1443], DS129[1444], DS129[1445], DS129[1446], DS129[1447], DS129[1448], DS129[1449], DS129[1450], DS129[1451], DS129[1452], DS129[1453], DS129[1454], DS129[1455], DS129[1456], DS129[1457], DS129[1458], DS129[1459], DS129[1460], DS129[1461], DS129[1462], DS129[1463], DS129[1464], DS129[1465], DS129[1466]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,129].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,129] is 560
### The list of all inequivalent reversible (64,28,12) DSs in group [64,129] is 
  
  
RDS129:=[ [ 2, 3, 8, 9, 10, 13, 16, 17, 23, 27, 28, 32, 33, 35, 36, 39, 40, 44, 46, 47, 48, 49, 52, 54, 56, 57, 59, 64 ], [ 2, 3, 8, 9, 10, 13, 16, 17, 23, 25, 28, 32, 33, 35, 36, 39, 40, 43, 47, 50, 52, 54, 56, 57, 60, 61, 62, 64 ], [ 2, 3, 8, 9, 10, 13, 16, 17, 23, 25, 27, 28, 32, 33, 35, 36, 39, 40, 43, 47, 49, 52, 54, 56, 57, 60, 61, 64 ], [ 2, 3, 8, 9, 10, 13, 14, 16, 17, 25, 28, 32, 35, 37, 39, 40, 44, 45, 47, 50, 52, 53, 57, 58, 59, 61, 62, 63 ], [ 2, 3, 8, 9, 10, 13, 14, 16, 17, 23, 25, 28, 32, 35, 37, 39, 40, 43, 47, 50, 52, 53, 57, 60, 61, 62, 63, 64 ], [ 2, 3, 8, 9, 10, 13, 14, 16, 17, 23, 25, 27, 28, 32, 35, 37, 39, 40, 43, 47, 49, 52, 53, 57, 60, 61, 63, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 16, 17, 28, 30, 33, 35, 36, 39, 40, 44, 45, 46, 47, 48, 50, 54, 56, 57, 58, 59, 62 ], [ 2, 3, 8, 9, 10, 11, 13, 16, 17, 23, 28, 30, 33, 35, 36, 39, 40, 43, 46, 47, 48, 50, 54, 56, 57, 60, 62, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 28, 30, 35, 37, 39, 40, 44, 45, 46, 47, 48, 50, 53, 57, 58, 59, 62, 63 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 28, 30, 35, 37, 39, 40, 43, 46, 47, 48, 50, 53, 57, 60, 62, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 16, 17, 20, 22, 27, 28, 32, 36, 39, 40, 42, 43, 45, 46, 47, 48, 49, 52, 56, 57, 58, 60 ], [ 2, 3, 6, 8, 9, 10, 16, 17, 20, 22, 23, 28, 32, 36, 39, 40, 42, 44, 46, 47, 48, 50, 52, 56, 57, 59, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 16, 17, 20, 22, 23, 27, 28, 32, 36, 39, 40, 42, 44, 46, 47, 48, 49, 52, 56, 57, 59, 64 ], [ 2, 3, 6, 8, 9, 10, 16, 17, 20, 22, 23, 25, 28, 32, 36, 39, 40, 42, 43, 47, 50, 52, 56, 57, 60, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 16, 17, 20, 22, 23, 25, 27, 28, 32, 36, 39, 40, 42, 43, 47, 49, 52, 56, 57, 60, 61, 64 ], [ 2, 3, 6, 8, 9, 10, 13, 16, 17, 22, 27, 28, 32, 33, 34, 35, 40, 43, 45, 46, 47, 48, 49, 52, 54, 55, 58, 60 ], [ 2, 3, 6, 8, 9, 10, 13, 16, 17, 22, 25, 28, 32, 33, 34, 35, 40, 44, 45, 47, 50, 52, 54, 55, 58, 59, 61, 62 ], [ 2, 3, 6, 8, 9, 10, 13, 16, 17, 22, 23, 28, 32, 33, 34, 35, 40, 44, 46, 47, 48, 50, 52, 54, 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