Graph forms
for C4 [ 256, 27 ] = MSZ(16,16,3,7)
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On this page are computer-accessible forms for the graph C4[ 256, 27 ] =
MSZ(16,16,3,7).
(I) Following is a form readable by MAGMA:
g:=Graph<256|{ {2, 3}, {254, 255}, {252, 253}, {250, 251}, {248, 249}, {246,
247}, {244, 245}, {242, 243}, {238, 239}, {236, 237}, {234, 235}, {232, 233},
{230, 231}, {228, 229}, {226, 227}, {222, 223}, {220, 221}, {218, 219}, {216,
217}, {214, 215}, {212, 213}, {210, 211}, {206, 207}, {204, 205}, {202, 203},
{100, 101}, {98, 99}, {94, 95}, {92, 93}, {90, 91}, {88, 89}, {86, 87}, {84,
85}, {82, 83}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {68, 69}, {66,
67}, {62, 63}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {18, 19},
{20, 21}, {22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {34, 35}, {36, 37},
{38, 39}, {40, 41}, {42, 43}, {44, 45}, {46, 47}, {50, 51}, {52, 53}, {54, 55},
{56, 57}, {58, 59}, {60, 61}, {102, 103}, {104, 105}, {106, 107}, {108, 109},
{110, 111}, {114, 115}, {116, 117}, {118, 119}, {120, 121}, {122, 123}, {124,
125}, {126, 127}, {130, 131}, {132, 133}, {134, 135}, {136, 137}, {138, 139},
{140, 141}, {142, 143}, {146, 147}, {148, 149}, {150, 151}, {152, 153}, {154,
155}, {156, 157}, {158, 159}, {162, 163}, {164, 165}, {166, 167}, {168, 169},
{170, 171}, {172, 173}, {174, 175}, {178, 179}, {180, 181}, {182, 183}, {184,
185}, {186, 187}, {188, 189}, {190, 191}, {194, 195}, {196, 197}, {198, 199},
{200, 201}, {1, 2}, {253, 254}, {249, 250}, {245, 246}, {241, 242}, {240, 243},
{237, 238}, {233, 234}, {229, 230}, {225, 226}, {224, 227}, {221, 222}, {217,
218}, {213, 214}, {209, 210}, {208, 211}, {205, 206}, {97, 98}, {96, 99}, {93,
94}, {89, 90}, {85, 86}, {81, 82}, {80, 83}, {77, 78}, {73, 74}, {69, 70}, {65,
66}, {64, 67}, {61, 62}, {5, 6}, {9, 10}, {13, 14}, {16, 19}, {17, 18}, {21,
22}, {25, 26}, {29, 30}, {32, 35}, {33, 34}, {37, 38}, {41, 42}, {45, 46}, {48,
51}, {49, 50}, {53, 54}, {57, 58}, {101, 102}, {105, 106}, {109, 110}, {112,
115}, {113, 114}, {117, 118}, {121, 122}, {125, 126}, {128, 131}, {129, 130},
{133, 134}, {137, 138}, {141, 142}, {144, 147}, {145, 146}, {149, 150}, {153,
154}, {157, 158}, {160, 163}, {161, 162}, {165, 166}, {169, 170}, {173, 174},
{176, 179}, {177, 178}, {181, 182}, {185, 186}, {189, 190}, {192, 195}, {193,
194}, {197, 198}, {201, 202}, {3, 4}, {251, 252}, {243, 244}, {235, 236}, {227,
228}, {219, 220}, {211, 212}, {203, 204}, {99, 100}, {91, 92}, {83, 84}, {75,
76}, {67, 68}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {43, 44}, {51, 52}, {59,
60}, {107, 108}, {115, 116}, {123, 124}, {131, 132}, {139, 140}, {147, 148},
{155, 156}, {163, 164}, {171, 172}, {179, 180}, {187, 188}, {195, 196}, {7, 8},
{247, 248}, {231, 232}, {215, 216}, {87, 88}, {71, 72}, {23, 24}, {39, 40}, {55,
56}, {103, 104}, {119, 120}, {135, 136}, {151, 152}, {167, 168}, {183, 184},
{199, 200}, {1, 16}, {225, 240}, {97, 112}, {65, 80}, {33, 48}, {129, 144},
{161, 176}, {193, 208}, {4, 23}, {236, 255}, {232, 251}, {228, 247}, {204, 223},
{100, 119}, {76, 95}, {72, 91}, {68, 87}, {8, 27}, {12, 31}, {36, 55}, {40, 59},
{44, 63}, {104, 123}, {108, 127}, {132, 151}, {136, 155}, {140, 159}, {164,
183}, {168, 187}, {172, 191}, {196, 215}, {200, 219}, {2, 21}, {234, 253}, {226,
245}, {202, 221}, {98, 117}, {74, 93}, {66, 85}, {10, 29}, {34, 53}, {42, 61},
{106, 125}, {130, 149}, {138, 157}, {162, 181}, {170, 189}, {194, 213}, {6, 25},
{239, 240}, {238, 241}, {230, 249}, {207, 208}, {206, 209}, {79, 80}, {78, 81},
{70, 89}, {14, 17}, {15, 16}, {38, 57}, {46, 49}, {47, 48}, {102, 121}, {110,
113}, {111, 112}, {134, 153}, {142, 145}, {143, 144}, {166, 185}, {174, 177},
{175, 176}, {198, 217}, {17, 32}, {209, 224}, {81, 96}, {145, 160}, {20, 39},
{220, 239}, {216, 235}, {212, 231}, {92, 111}, {88, 107}, {84, 103}, {24, 43},
{28, 47}, {148, 167}, {152, 171}, {156, 175}, {18, 37}, {218, 237}, {210, 229},
{90, 109}, {82, 101}, {26, 45}, {146, 165}, {154, 173}, {22, 41}, {223, 224},
{222, 225}, {214, 233}, {95, 96}, {94, 97}, {86, 105}, {30, 33}, {31, 32}, {150,
169}, {158, 161}, {159, 160}, {49, 64}, {177, 192}, {52, 71}, {56, 75}, {60,
79}, {180, 199}, {184, 203}, {188, 207}, {1, 116}, {3, 118}, {9, 124}, {11,
126}, {129, 244}, {131, 246}, {137, 252}, {139, 254}, {50, 69}, {58, 77}, {178,
197}, {186, 205}, {5, 120}, {7, 122}, {15, 114}, {133, 248}, {135, 250}, {143,
242}, {54, 73}, {63, 64}, {62, 65}, {182, 201}, {190, 193}, {191, 192}, {13,
128}, {96, 237}, {93, 208}, {80, 221}, {77, 192}, {64, 205}, {61, 176}, {16,
157}, {29, 144}, {32, 173}, {45, 160}, {48, 189}, {109, 224}, {112, 253}, {125,
240}, {4, 145}, {100, 241}, {91, 206}, {89, 204}, {83, 198}, {81, 196}, {78,
219}, {76, 217}, {70, 211}, {68, 209}, {6, 147}, {12, 153}, {14, 155}, {17,
132}, {19, 134}, {25, 140}, {27, 142}, {36, 177}, {38, 179}, {44, 185}, {46,
187}, {49, 164}, {51, 166}, {57, 172}, {59, 174}, {102, 243}, {108, 249}, {110,
251}, {113, 228}, {115, 230}, {121, 236}, {123, 238}, {2, 159}, {98, 255}, {95,
194}, {87, 202}, {85, 200}, {74, 215}, {72, 213}, {66, 223}, {63, 162}, {8,
149}, {10, 151}, {21, 136}, {23, 138}, {31, 130}, {34, 191}, {40, 181}, {42,
183}, {53, 168}, {55, 170}, {104, 245}, {106, 247}, {117, 232}, {119, 234},
{127, 226}, {20, 161}, {99, 214}, {97, 212}, {94, 235}, {92, 233}, {86, 227},
{84, 225}, {22, 163}, {28, 169}, {30, 171}, {33, 148}, {35, 150}, {41, 156},
{43, 158}, {105, 220}, {107, 222}, {18, 175}, {90, 231}, {88, 229}, {82, 239},
{24, 165}, {26, 167}, {37, 152}, {39, 154}, {47, 146}, {101, 216}, {103, 218},
{111, 210}, {113, 128}, {7, 244}, {11, 248}, {15, 252}, {116, 135}, {120, 139},
{124, 143}, {52, 193}, {75, 190}, {73, 188}, {67, 182}, {65, 180}, {62, 203},
{54, 195}, {60, 201}, {5, 242}, {13, 250}, {114, 133}, {122, 141}, {50, 207},
{79, 178}, {71, 186}, {69, 184}, {56, 197}, {58, 199}, {1, 254}, {9, 246}, {118,
137}, {126, 129}, {127, 128}, {3, 256}, {141, 256}, {241, 256}, {255, 256}
}>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 254)(3, 139)(4, 120)(6, 242)(7, 143)(8, 124)(10, 246)(11, 131)(12,
128)(14, 250)(15, 135)(16, 116)(17, 249)(18, 230)(19, 115)(20, 112)(21, 253)(22,
234)(23, 119)(24, 100)(25, 241)(26, 238)(27, 123)(28, 104)(29, 245)(30, 226)(31,
127)(32, 108)(33, 225)(34, 222)(35, 107)(36, 88)(37, 229)(38, 210)(39, 111)(40,
92)(41, 233)(42, 214)(43, 99)(44, 96)(45, 237)(46, 218)(47, 103)(48, 84)(49,
217)(50, 198)(51, 83)(52, 80)(53, 221)(54, 202)(55, 87)(56, 68)(57, 209)(58,
206)(59, 91)(60, 72)(61, 213)(62, 194)(63, 95)(64, 76)(65, 193)(66, 190)(67,
75)(69, 197)(70, 178)(71, 79)(73, 201)(74, 182)(77, 205)(78, 186)(81, 185)(82,
166)(85, 189)(86, 170)(89, 177)(90, 174)(93, 181)(94, 162)(97, 161)(98,
158)(101, 165)(102, 146)(105, 169)(106, 150)(109, 173)(110, 154)(113, 153)(114,
134)(117, 157)(118, 138)(121, 145)(122, 142)(125, 149)(126, 130)(132, 248)(136,
252)(140, 256)(144, 244)(147, 243)(148, 240)(151, 247)(152, 228)(155, 251)(156,
232)(159, 255)(160, 236)(163, 235)(164, 216)(167, 239)(168, 220)(171, 227)(172,
224)(175, 231)(176, 212)(179, 211)(180, 208)(183, 215)(184, 196)(187, 219)(188,
200)(191, 223)(192, 204)(195, 203)(199, 207) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (2, 116)(3, 135)(4, 250)(5, 13)(6, 128)(7, 131)(8, 246)(10, 124)(11, 143)(12,
242)(14, 120)(15, 139)(16, 254)(17, 121)(18, 236)(19, 255)(20, 98)(21, 117)(22,
232)(23, 251)(24, 110)(25, 113)(26, 228)(27, 247)(28, 106)(29, 125)(30, 240)(31,
243)(32, 102)(33, 225)(34, 84)(35, 103)(36, 218)(37, 237)(38, 96)(39, 99)(40,
214)(41, 233)(42, 92)(43, 111)(44, 210)(45, 229)(46, 88)(47, 107)(48, 222)(49,
89)(50, 204)(51, 223)(52, 66)(53, 85)(54, 200)(55, 219)(56, 78)(57, 81)(58,
196)(59, 215)(60, 74)(61, 93)(62, 208)(63, 211)(64, 70)(65, 193)(67, 71)(68,
186)(69, 205)(72, 182)(73, 201)(75, 79)(76, 178)(77, 197)(80, 190)(82, 172)(83,
191)(86, 168)(87, 187)(90, 164)(91, 183)(94, 176)(95, 179)(97, 161)(100,
154)(101, 173)(104, 150)(105, 169)(108, 146)(109, 165)(112, 158)(114, 140)(115,
159)(118, 136)(119, 155)(122, 132)(123, 151)(126, 144)(127, 147)(130, 244)(133,
141)(134, 256)(138, 252)(142, 248)(145, 249)(148, 226)(149, 245)(152, 238)(153,
241)(156, 234)(157, 253)(160, 230)(162, 212)(163, 231)(166, 224)(167, 227)(170,
220)(171, 239)(174, 216)(175, 235)(177, 217)(180, 194)(181, 213)(184, 206)(185,
209)(188, 202)(189, 221)(192, 198)(195, 199)(203, 207)
c: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)(17, 114, 19, 116, 21,
118, 23, 120, 25, 122, 27, 124, 29, 126, 31, 128)(18, 115, 20, 117, 22, 119, 24,
121, 26, 123, 28, 125, 30, 127, 32, 113)(33, 226, 35, 228, 37, 230, 39, 232, 41,
234, 43, 236, 45, 238, 47, 240)(34, 227, 36, 229, 38, 231, 40, 233, 42, 235, 44,
237, 46, 239, 48, 225)(49, 82, 51, 84, 53, 86, 55, 88, 57, 90, 59, 92, 61, 94,
63, 96)(50, 83, 52, 85, 54, 87, 56, 89, 58, 91, 60, 93, 62, 95, 64, 81)(65, 194,
67, 196, 69, 198, 71, 200, 73, 202, 75, 204, 77, 206, 79, 208)(66, 195, 68, 197,
70, 199, 72, 201, 74, 203, 76, 205, 78, 207, 80, 193)(97, 162, 99, 164, 101,
166, 103, 168, 105, 170, 107, 172, 109, 174, 111, 176)(98, 163, 100, 165, 102,
167, 104, 169, 106, 171, 108, 173, 110, 175, 112, 161)(129, 130, 131, 132, 133,
134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144)(145, 242, 147, 244, 149,
246, 151, 248, 153, 250, 155, 252, 157, 254, 159, 256)(146, 243, 148, 245, 150,
247, 152, 249, 154, 251, 156, 253, 158, 255, 160, 241)(177, 210, 179, 212, 181,
214, 183, 216, 185, 218, 187, 220, 189, 222, 191, 224)(178, 211, 180, 213, 182,
215, 184, 217, 186, 219, 188, 221, 190, 223, 192, 209)
C4[ 256, 27 ]
256
-1 254 2 16 116
-2 1 3 159 21
-3 2 256 4 118
-4 23 145 3 5
-5 242 4 6 120
-6 25 147 5 7
-7 122 244 6 8
-8 27 149 7 9
-9 124 246 8 10
-10 11 29 151 9
-11 12 126 248 10
-12 11 13 31 153
-13 12 14 128 250
-14 155 13 15 17
-15 14 114 16 252
-16 1 157 15 19
-17 132 14 18 32
-18 37 17 19 175
-19 134 16 18 20
-20 39 161 19 21
-21 22 2 136 20
-22 23 41 163 21
-23 22 24 4 138
-24 165 23 25 43
-25 24 26 6 140
-26 45 167 25 27
-27 26 28 8 142
-28 47 169 27 29
-29 144 28 30 10
-30 33 171 29 31
-31 12 30 130 32
-32 35 17 173 31
-33 34 48 148 30
-34 33 35 191 53
-35 34 36 150 32
-36 55 177 35 37
-37 36 38 18 152
-38 57 179 37 39
-39 154 38 40 20
-40 59 181 39 41
-41 22 156 40 42
-42 61 183 41 43
-43 44 24 158 42
-44 45 63 185 43
-45 44 46 26 160
-46 187 45 47 49
-47 46 146 48 28
-48 33 189 47 51
-49 46 50 64 164
-50 69 49 51 207
-51 166 48 50 52
-52 71 193 51 53
-53 34 168 52 54
-54 55 73 195 53
-55 56 36 170 54
-56 55 57 75 197
-57 56 58 38 172
-58 77 199 57 59
-59 58 60 40 174
-60 79 201 59 61
-61 176 60 62 42
-62 203 61 63 65
-63 44 62 162 64
-64 67 49 205 63
-65 66 80 180 62
-66 67 223 85 65
-67 66 68 182 64
-68 209 67 69 87
-69 68 70 50 184
-70 89 211 69 71
-71 70 72 52 186
-72 91 213 71 73
-73 188 72 74 54
-74 93 215 73 75
-75 56 190 74 76
-76 77 95 217 75
-77 78 58 192 76
-78 77 79 81 219
-79 78 178 80 60
-80 221 79 83 65
-81 78 82 96 196
-82 101 81 83 239
-83 198 80 82 84
-84 103 225 83 85
-85 66 200 84 86
-86 105 227 85 87
-87 88 68 202 86
-88 89 107 229 87
-89 88 90 70 204
-90 231 89 91 109
-91 90 92 72 206
-92 111 233 91 93
-93 92 94 74 208
-94 235 93 95 97
-95 94 194 96 76
-96 99 81 237 95
-97 112 212 94 98
-98 99 255 117 97
-99 100 214 96 98
-100 99 101 119 241
-101 100 102 82 216
-102 121 243 101 103
-103 102 104 84 218
-104 123 245 103 105
-105 220 104 106 86
-106 125 247 105 107
-107 88 222 106 108
-108 127 249 107 109
-109 110 90 224 108
-110 111 113 251 109
-111 110 210 112 92
-112 253 111 115 97
-113 110 114 128 228
-114 133 113 15 115
-115 112 114 116 230
-116 1 135 115 117
-117 232 116 118 98
-118 3 137 117 119
-119 100 234 118 120
-120 121 5 139 119
-121 122 102 236 120
-122 121 123 7 141
-123 122 124 104 238
-124 143 123 125 9
-125 124 126 106 240
-126 11 125 127 129
-127 126 226 128 108
-128 13 113 127 131
-129 144 244 126 130
-130 149 129 31 131
-131 132 246 128 130
-132 133 17 151 131
-133 132 134 114 248
-134 133 135 19 153
-135 134 136 116 250
-136 155 135 137 21
-137 136 138 118 252
-138 23 157 137 139
-139 254 138 140 120
-140 25 159 139 141
-141 122 256 140 142
-142 143 145 27 141
-143 242 144 124 142
-144 143 147 29 129
-145 146 4 160 142
-146 165 145 47 147
-147 144 146 148 6
-148 33 167 147 149
-149 148 150 8 130
-150 35 169 149 151
-151 132 150 152 10
-152 37 171 151 153
-153 154 12 134 152
-154 155 39 173 153
-155 154 156 14 136
-156 155 157 41 175
-157 156 158 16 138
-158 157 159 161 43
-159 2 158 160 140
-160 45 145 159 163
-161 176 158 162 20
-162 181 161 63 163
-163 22 160 162 164
-164 165 49 183 163
-165 166 24 146 164
-166 165 167 51 185
-167 166 168 26 148
-168 187 167 169 53
-169 168 170 28 150
-170 55 189 169 171
-171 170 172 30 152
-172 57 191 171 173
-173 154 172 174 32
-174 177 59 173 175
-175 176 156 18 174
-176 179 61 161 175
-177 178 36 192 174
-178 177 79 179 197
-179 176 178 180 38
-180 199 179 181 65
-181 180 182 40 162
-182 67 201 181 183
-183 182 184 42 164
-184 69 203 183 185
-185 44 166 184 186
-186 187 71 205 185
-187 188 46 168 186
-188 187 189 73 207
-189 188 190 48 170
-190 189 191 193 75
-191 34 190 192 172
-192 77 177 191 195
-193 190 194 52 208
-194 213 193 95 195
-195 192 194 196 54
-196 81 215 195 197
-197 198 56 178 196
-198 199 83 217 197
-199 198 200 58 180
-200 199 201 85 219
-201 200 202 60 182
-202 221 201 203 87
-203 202 204 62 184
-204 89 223 203 205
-205 204 206 64 186
-206 209 91 205 207
-207 188 50 206 208
-208 211 93 193 207
-209 210 68 224 206
-210 209 111 211 229
-211 210 212 70 208
-212 231 211 213 97
-213 212 214 72 194
-214 99 233 213 215
-215 214 216 74 196
-216 101 235 215 217
-217 198 216 218 76
-218 103 237 217 219
-219 220 78 200 218
-220 221 105 239 219
-221 220 222 80 202
-222 221 223 225 107
-223 66 222 224 204
-224 209 223 227 109
-225 222 226 84 240
-226 245 225 127 227
-227 224 226 228 86
-228 113 247 227 229
-229 88 210 228 230
-230 231 115 249 229
-231 232 90 212 230
-232 231 233 117 251
-233 232 234 92 214
-234 253 233 235 119
-235 234 236 94 216
-236 121 255 235 237
-237 236 238 96 218
-238 123 237 239 241
-239 220 82 238 240
-240 243 125 225 239
-241 242 100 256 238
-242 143 243 5 241
-243 242 244 102 240
-244 243 245 7 129
-245 244 246 104 226
-246 245 247 9 131
-247 246 248 106 228
-248 11 133 247 249
-249 248 250 108 230
-250 13 135 249 251
-251 110 232 250 252
-252 253 15 137 251
-253 254 112 234 252
-254 253 1 255 139
-255 254 256 236 98
-256 255 3 141 241
0