### 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 [64,150]. 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 [64,150].
    
    
# 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(64,150));' can be 
# used to create a list e of the elements of the group [64,150].
# In our list of (64,28,12) DSs in group [64,150], we have [1, 
# 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 27, 29, 
# 30, 34, 35, 38, 40, 43, 50, 52, 55, 56, 57, 60, 64].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[6], e[9], e[12], e[13], e[14], e[18], e[20], e[23], e[27], e[29], e[30], 
# e[34], e[35], e[38], e[40], e[43], e[50], e[52], e[55], e[56], e[57], e[60], e[64]]
# where e is the list of the elements of the group [64,150] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,150));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 150]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,150] is 288
### The list of all inequivalent (64,28,12) DSs in group [64,150] is 
  
  
DS150:=[ [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 27, 29, 30, 34, 35, 38, 40, 43, 50, 52, 55, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 16, 17, 20, 23, 27, 29, 32, 33, 36, 41, 43, 44, 50, 52, 53, 54, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 16, 17, 20, 23, 29, 32, 33, 37, 41, 43, 44, 49, 52, 53, 54, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 16, 20, 23, 27, 29, 32, 34, 35, 36, 39, 40, 41, 43, 44, 50, 52, 55, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 16, 20, 23, 29, 32, 34, 35, 37, 39, 40, 41, 43, 44, 49, 52, 55, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 20, 23, 29, 31, 34, 35, 38, 40, 43, 49, 55, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 16, 20, 23, 25, 26, 30, 31, 32, 33, 35, 36, 39, 40, 41, 43, 44, 48, 54, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 16, 17, 20, 23, 25, 26, 30, 31, 32, 33, 35, 36, 41, 43, 44, 48, 54, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 16, 20, 23, 25, 26, 30, 31, 32, 35, 37, 39, 40, 41, 43, 44, 48, 53, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 16, 17, 20, 23, 25, 26, 30, 31, 32, 35, 37, 41, 43, 44, 48, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 20, 23, 25, 26, 30, 38, 40, 43, 45, 48, 52, 53, 54, 55, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 20, 23, 24, 26, 30, 38, 40, 44, 45, 47, 52, 53, 54, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 20, 23, 24, 26, 30, 34, 35, 38, 40, 43, 47, 52, 55, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 19, 20, 23, 24, 26, 30, 38, 41, 43, 44, 47, 52, 53, 54, 55, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 19, 20, 23, 25, 26, 30, 38, 40, 44, 48, 52, 53, 54, 55, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 19, 20, 23, 25, 26, 30, 38, 40, 43, 44, 48, 52, 53, 54, 55, 56, 58 ], [ 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, 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, 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, 16, 17, 19, 20, 23, 24, 32, 33, 36, 40, 44, 48, 55, 56, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 16, 17, 19, 20, 23, 24, 32, 33, 36, 40, 43, 44, 48, 55, 56, 58, 61, 63 ], [ 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, 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, 18, 20, 23, 24, 26, 32, 35, 38, 40, 47, 53, 56, 57, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 23, 24, 26, 32, 35, 38, 40, 43, 47, 53, 56, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 19, 20, 23, 26, 32, 38, 40, 44, 46, 53, 54, 55, 56, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 19, 20, 23, 26, 32, 38, 40, 43, 44, 46, 53, 54, 55, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 19, 20, 23, 24, 32, 33, 37, 39, 44, 48, 55, 57, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 19, 20, 23, 24, 32, 33, 37, 39, 43, 44, 48, 55, 57, 58, 61, 63 ], [ 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, 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, 10, 16, 20, 23, 24, 26, 32, 33, 36, 39, 40, 41, 43, 44, 47, 52, 53, 54, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 16, 17, 20, 23, 24, 26, 32, 33, 36, 41, 43, 44, 47, 52, 53, 54, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 14, 16, 20, 23, 26, 32, 33, 37, 39, 40, 41, 43, 44, 46, 52, 53, 54, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 14, 16, 17, 20, 23, 26, 32, 33, 37, 41, 43, 44, 46, 52, 53, 54, 57, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20, 23, 25, 26, 32, 33, 35, 36, 39, 40, 41, 43, 44, 48, 52, 54, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20, 23, 24, 26, 32, 34, 35, 36, 39, 40, 41, 43, 44, 47, 52, 55, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 17, 20, 23, 25, 26, 32, 33, 35, 36, 41, 43, 44, 48, 52, 54, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 17, 20, 23, 24, 26, 32, 34, 35, 36, 41, 43, 44, 47, 52, 55, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 15, 16, 20, 23, 26, 32, 33, 35, 38, 39, 40, 41, 43, 44, 46, 52, 54, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 15, 16, 20, 23, 24, 26, 32, 35, 38, 39, 40, 41, 43, 44, 47, 52, 53, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 15, 16, 17, 20, 23, 26, 32, 33, 35, 38, 41, 43, 44, 46, 52, 54, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 15, 16, 17, 20, 23, 24, 26, 32, 35, 38, 41, 43, 44, 47, 52, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 20, 23, 26, 32, 34, 35, 37, 39, 40, 41, 43, 44, 46, 52, 55, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 20, 23, 25, 26, 32, 35, 37, 39, 40, 41, 43, 44, 48, 52, 53, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 17, 20, 23, 26, 32, 34, 35, 37, 41, 43, 44, 46, 52, 55, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 13, 14, 16, 17, 20, 23, 25, 26, 32, 35, 37, 41, 43, 44, 48, 52, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 20, 23, 26, 31, 38, 40, 44, 45, 46, 53, 54, 55, 56, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 20, 23, 26, 31, 34, 35, 38, 40, 43, 46, 55, 56, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 20, 23, 25, 26, 31, 38, 40, 45, 48, 53, 54, 55, 56, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 20, 23, 25, 26, 31, 35, 38, 40, 48, 53, 56, 57, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 20, 23, 25, 26, 31, 35, 38, 40, 43, 48, 53, 56, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 19, 20, 23, 26, 31, 38, 41, 43, 44, 46, 53, 54, 55, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 19, 20, 24, 26, 32, 33, 34, 35, 38, 39, 45, 47, 51, 53, 54, 57, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 19, 20, 23, 24, 26, 32, 33, 34, 35, 38, 39, 43, 44, 47, 51, 53, 54, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 18, 20, 26, 27, 32, 34, 35, 38, 40, 44, 46, 49, 50, 51, 57, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 18, 20, 24, 26, 27, 32, 34, 35, 38, 40, 43, 44, 47, 49, 50, 51, 57, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 18, 20, 23, 26, 27, 32, 34, 35, 38, 40, 43, 45, 46, 49, 50, 51, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 18, 20, 23, 24, 26, 27, 32, 34, 35, 38, 40, 45, 47, 49, 50, 51, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 17, 19, 20, 26, 32, 33, 34, 35, 38, 40, 45, 46, 51, 53, 54, 59, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 17, 19, 20, 23, 26, 32, 33, 34, 35, 38, 40, 43, 44, 46, 51, 53, 54, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 16, 20, 23, 25, 26, 27, 29, 30, 31, 32, 36, 39, 40, 41, 43, 44, 48, 50, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 16, 18, 20, 25, 26, 27, 30, 31, 32, 34, 36, 40, 48, 51, 53, 55, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 16, 18, 20, 23, 25, 26, 27, 30, 31, 32, 36, 40, 43, 45, 48, 51, 56, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 16, 17, 20, 23, 25, 26, 27, 29, 30, 31, 32, 36, 41, 43, 44, 48, 50, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 16, 17, 19, 20, 23, 25, 26, 27, 30, 31, 32, 36, 40, 43, 44, 48, 51, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 19, 20, 24, 26, 32, 34, 35, 36, 37, 38, 39, 45, 47, 51, 56, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 19, 20, 23, 24, 26, 32, 34, 35, 36, 37, 38, 39, 44, 47, 51, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 19, 20, 23, 24, 26, 32, 34, 35, 36, 37, 38, 39, 43, 44, 47, 51, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 18, 20, 26, 32, 34, 35, 36, 37, 38, 40, 44, 46, 51, 56, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 18, 20, 24, 26, 32, 34, 35, 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1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 18, 20, 22, 30, 33, 35, 36, 43, 48, 49, 50, 51, 52, 54, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 16, 21, 23, 29, 31, 32, 34, 38, 40, 42, 46, 49, 51, 53, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 16, 19, 21, 22, 27, 28, 31, 36, 37, 48, 49, 52, 53, 55, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 16, 19, 21, 22, 27, 28, 31, 43, 48, 49, 52, 53, 55, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 16, 21, 29, 30, 33, 34, 40, 42, 43, 51, 53, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 19, 21, 22, 23, 25, 32, 43, 44, 47, 49, 50, 51, 52, 53, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 19, 21, 22, 23, 24, 25, 32, 44, 46, 49, 50, 51, 52, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 22, 26, 27, 29, 31, 32, 35, 37, 41, 42, 54, 55, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 22, 26, 27, 28, 30, 32, 33, 41, 42, 44, 46, 53, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 22, 23, 26, 27, 28, 30, 32, 33, 41, 42, 43, 45, 46, 53, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 22, 26, 27, 29, 31, 32, 33, 35, 36, 41, 42, 53, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 16, 18, 20, 22, 27, 29, 32, 34, 36, 43, 48, 50, 52, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 16, 18, 20, 22, 25, 32, 33, 35, 36, 43, 49, 50, 51, 52, 54, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 22, 26, 27, 29, 31, 32, 33, 34, 37, 41, 42, 53, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 16, 18, 20, 22, 29, 32, 34, 37, 43, 48, 49, 52, 54, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 16, 18, 20, 22, 25, 32, 35, 37, 43, 49, 50, 51, 52, 53, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 22, 26, 27, 29, 31, 32, 34, 36, 41, 42, 54, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 20, 22, 29, 32, 33, 35, 36, 43, 48, 49, 52, 54, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 20, 22, 27, 29, 32, 35, 36, 43, 48, 50, 52, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 22, 23, 25, 29, 31, 38, 43, 46, 47, 49, 53, 54, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 22, 23, 24, 25, 29, 31, 33, 38, 43, 49, 58, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 17, 18, 19, 26, 30, 32, 34, 37, 43, 44, 48, 52, 58, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 18, 20, 22, 25, 29, 31, 33, 36, 37, 38, 43, 49, 55, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 22, 25, 28, 31, 36, 41, 42, 43, 50, 53, 54, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 18, 20, 22, 31, 34, 36, 43, 48, 49, 50, 51, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 22, 25, 28, 31, 35, 38, 41, 42, 43, 50, 53, 56, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 18, 20, 22, 25, 29, 31, 38, 43, 49, 53, 54, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 22, 31, 35, 36, 43, 48, 49, 50, 51, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 24, 25, 30, 31, 32, 34, 37, 40, 41, 43, 48, 49, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 24, 25, 26, 27, 32, 34, 37, 40, 41, 45, 46, 49, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 23, 24, 30, 31, 32, 34, 37, 40, 41, 45, 46, 49, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 25, 43, 44, 45, 47, 50, 51, 52, 53, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 25, 27, 43, 44, 45, 47, 49, 51, 52, 53, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 25, 27, 30, 44, 45, 51, 53, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 28, 30, 43, 46, 47, 48, 50, 53, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 25, 47, 50, 51, 52, 53, 58, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 25, 27, 47, 49, 51, 52, 53, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 43, 44, 48, 50, 51, 52, 53, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 28, 30, 48, 50, 53, 58, 59, 60, 61, 62, 63 ], [ 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, 43, 51, 53, 58, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 21, 23, 29, 32, 33, 35, 38, 40, 42, 51, 53, 54, 56, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 20, 21, 23, 29, 32, 33, 37, 46, 51, 53, 55, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 25, 30, 31, 32, 34, 40, 41, 43, 47, 48, 49, 53, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 24, 25, 27, 32, 34, 40, 41, 43, 47, 48, 49, 53, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 23, 27, 32, 34, 40, 41, 43, 45, 49, 53, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 23, 26, 31, 32, 34, 40, 41, 43, 48, 52, 53, 58, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 23, 29, 32, 34, 35, 39, 40, 51, 53, 54, 55, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 17, 23, 29, 32, 35, 36, 38, 39, 40, 51, 54, 56, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 23, 29, 32, 37, 39, 40, 46, 51, 53, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 20, 21, 23, 29, 32, 51, 53, 54, 55, 61, 62, 63, 64 ], [ 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, 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, 22, 25, 27, 29, 30, 35, 38, 41, 42, 43, 50, 53, 56, 58, 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, 19, 21, 22, 28, 30, 43, 48, 50, 53, 55, 56, 62, 63, 64 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 175
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS150[2], DS150[3], DS150[4], DS150[5], DS150[7], DS150[8], DS150[9], DS150[10], DS150[12], DS150[13], DS150[14], DS150[15], DS150[16], DS150[21], DS150[22], DS150[23], DS150[25], DS150[26], DS150[28], DS150[30], DS150[31], DS150[32], DS150[35], DS150[36], DS150[37], DS150[38], DS150[39], DS150[40], DS150[41], DS150[42], DS150[43], DS150[44], DS150[45], DS150[46], DS150[47], DS150[48], DS150[49], DS150[50], DS150[52], DS150[54], DS150[55], DS150[56], DS150[58], DS150[65], DS150[66], DS150[68], DS150[69], DS150[80], DS150[81], DS150[84], DS150[87], DS150[93], DS150[97], DS150[100], DS150[101], DS150[102], DS150[104], DS150[105], DS150[108], DS150[110], DS150[111], DS150[112], DS150[115], DS150[116], DS150[117], DS150[118], DS150[120], DS150[121], DS150[123], DS150[124], DS150[127], DS150[128], DS150[130], DS150[135], DS150[138], DS150[140], DS150[141], DS150[144], DS150[146], DS150[147], DS150[148], DS150[150], DS150[152], DS150[154], DS150[155], DS150[156], DS150[157], DS150[158], DS150[159], DS150[160], DS150[161], DS150[167], DS150[168], DS150[169], DS150[170], DS150[172], DS150[173], DS150[174], DS150[175], DS150[179], DS150[180], DS150[181], DS150[182], DS150[183], DS150[184], DS150[187], DS150[188], DS150[190], DS150[195], DS150[196], DS150[197], DS150[198], DS150[200], DS150[201], DS150[203], DS150[205], DS150[207], DS150[208], DS150[209], DS150[210], DS150[211], DS150[212], DS150[213], DS150[215], DS150[226], DS150[227], DS150[228], DS150[230], DS150[231], DS150[232], DS150[233], DS150[234], DS150[235], DS150[236], DS150[239], DS150[240], DS150[241], DS150[242], DS150[243], DS150[245], DS150[246], DS150[248], DS150[249], DS150[250], DS150[251], DS150[252], DS150[253], DS150[255], DS150[256], DS150[257], DS150[259], DS150[260], DS150[261], DS150[262], DS150[264], DS150[266], DS150[268], DS150[269], DS150[271], DS150[273], DS150[274], DS150[275], DS150[276], DS150[277], DS150[278], DS150[279], DS150[280], DS150[281], DS150[282], DS150[283], DS150[284], DS150[285], DS150[286], DS150[287], DS150[288]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,150].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,150] is 212
### The list of all inequivalent reversible (64,28,12) DSs in group [64,150] is 
  
  
RDS150:=[ [ 2, 5, 6, 8, 9, 10, 11, 13, 17, 21, 22, 23, 24, 28, 30, 33, 35, 39, 40, 48, 50, 54, 57, 58, 59, 60, 61, 62 ], [ 2, 4, 6, 8, 9, 10, 11, 13, 19, 20, 22, 23, 24, 28, 30, 39, 42, 44, 45, 48, 50, 53, 54, 55, 57, 60, 61, 62 ], [ 2, 4, 6, 8, 9, 10, 11, 13, 19, 20, 22, 23, 24, 28, 29, 30, 34, 39, 42, 48, 51, 54, 57, 58, 59, 60, 61, 63 ], [ 2, 4, 5, 8, 9, 10, 11, 13, 19, 20, 21, 23, 28, 30, 33, 35, 39, 42, 43, 46, 47, 48, 50, 54, 57, 60, 62, 64 ], [ 2, 4, 5, 8, 9, 10, 11, 13, 19, 20, 21, 23, 24, 28, 30, 33, 35, 39, 42, 48, 50, 54, 57, 58, 59, 60, 61, 62 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 18, 19, 21, 22, 23, 24, 28, 30, 33, 35, 41, 48, 50, 54, 58, 59, 60, 61, 62 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 17, 19, 21, 22, 23, 24, 28, 30, 40, 44, 45, 48, 50, 53, 54, 55, 60, 61, 62 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 17, 19, 21, 22, 23, 24, 28, 29, 30, 34, 40, 48, 51, 54, 58, 59, 60, 61, 63 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 17, 26, 28, 30, 33, 35, 38, 39, 40, 43, 44, 45, 46, 50, 54, 56, 57, 61, 62, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 17, 23, 26, 28, 30, 33, 35, 38, 39, 40, 43, 46, 50, 54, 56, 57, 60, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 12, 13, 14, 15, 17, 20, 22, 24, 27, 28, 30, 36, 39, 40, 42, 48, 49, 52, 53, 54, 55, 57, 61 ], [ 2, 3, 6, 8, 9, 10, 11, 14, 17, 20, 22, 23, 26, 28, 30, 38, 39, 40, 42, 43, 46, 50, 56, 57, 60, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 20, 22, 26, 28, 30, 38, 42, 43, 46, 50, 53, 54, 55, 56, 58, 59, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 20, 22, 23, 26, 28, 30, 38, 42, 44, 45, 46, 50, 53, 54, 55, 56, 60, 61, 62 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 20, 22, 23, 26, 28, 29, 30, 34, 38, 42, 46, 51, 54, 56, 58, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 20, 22, 23, 26, 28, 29, 30, 34, 38, 42, 43, 46, 51, 54, 56, 60, 61, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 17, 20, 22, 26, 28, 30, 38, 39, 40, 42, 46, 50, 53, 54, 55, 56, 57, 61, 62 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 20, 21, 26, 28, 30, 33, 35, 38, 42, 43, 44, 45, 46, 50, 54, 56, 61, 62, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 20, 21, 23, 26, 28, 30, 33, 35, 38, 42, 43, 46, 50, 54, 56, 60, 61, 62, 64 ], [ 2, 3, 5, 6, 9, 10, 11, 13, 14, 17, 21, 22, 23, 28, 30, 33, 35, 38, 39, 40, 43, 50, 54, 56, 57, 60, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 11, 12, 13, 14, 15, 21, 22, 23, 24, 27, 28, 32, 33, 35, 36, 48, 49, 54, 58, 59, 60, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 21, 22, 24, 27, 28, 31, 36, 39, 40, 48, 49, 53, 54, 55, 57, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 17, 21, 22, 23, 24, 26, 28, 30, 38, 39, 40, 43, 47, 50, 56, 57, 60, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 17, 21, 22, 23, 24, 28, 30, 37, 39, 40, 48, 50, 57, 58, 59, 60, 61, 62 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 21, 22, 24, 26, 28, 30, 38, 43, 47, 50, 53, 54, 55, 56, 58, 59, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 21, 22, 23, 25, 26, 28, 30, 33, 35, 38, 43, 48, 50, 54, 56, 60, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 21, 22, 23, 24, 26, 28, 30, 38, 44, 45, 47, 50, 53, 54, 55, 56, 60, 62 ], [ 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