Optimal a-set pairs
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The row "a1 a3 x * y = xy" denotes the class of Level1, Level3 pairs, where Level1 is a 3D Moser set whose "a" points have signature a1 (when viewed as an 8-bit integer), and Level3 is a 3D Moser set whose "a" points have signature a3. x and y denote the number of 3D Moser sets with signature a1 and a3 respectively. There is one configuration per equivalence class (under the order 384 symmetry group of [math]\displaystyle{ [3]^4 }[/math]), and those configurations with a=1,2,3 have been deleted. Code for generating this list can be found here.
0 0 82173*82173 = 2457434633 0 15 82173*5750 = 472494750 0 23 82173*3071 = 252353283 0 27 82173*4021 = 330417633 0 30 82173*5000 = 410865000 0 31 82173*625 = 51358125 0 60 82173*9604 = 789189492 0 61 82173*784 = 64423632 0 63 82173*98 = 8052954 0 105 82173*4825 = 396484725 0 107 82173*512 = 42072576 0 111 82173*64 = 5259072 0 126 82173*64 = 5259072 0 127 82173*8 = 657384 0 255 82173*1 = 82173 1 22 82173*20472 = 1682245656 1 23 82173*3071 = 252353283 2 21 82173*16836 = 1383464628 2 22 82173*20472 = 1682245656 2 23 82173*3071 = 252353283 1 30 82173*5000 = 410865000 1 31 82173*625 = 51358125 1 44 82173*25777 = 2118173421 2 29 82173*4021 = 330417633 1 47 82173*625 = 51358125 1 60 82173*9604 = 789189492 1 61 82173*784 = 64423632 1 62 82173*784 = 64423632 1 63 82173*98 = 8052954 1 104 82173*20472 = 1682245656 1 105 82173*4825 = 396484725 1 106 82173*5000 = 410865000 1 107 82173*512 = 42072576 1 110 82173*784 = 64423632 1 111 82173*64 = 5259072 1 126 82173*64 = 5259072 1 127 82173*8 = 657384 8 19 82173*16836 = 1383464628 1 134 82173*20472 = 1682245656 8 23 82173*3071 = 252353283 1 137 82173*25777 = 2118173421 1 139 82173*4021 = 330417633 1 143 82173*625 = 51358125 1 150 82173*4825 = 396484725 1 151 82173*512 = 42072576 1 152 82173*25777 = 2118173421 1 153 82173*9604 = 789189492 1 154 82173*5000 = 410865000 1 155 82173*784 = 64423632 1 158 82173*512 = 42072576 1 159 82173*64 = 5259072 1 168 82173*16836 = 1383464628 1 169 82173*5000 = 410865000 1 170 82173*5750 = 472494750 1 171 82173*625 = 51358125 1 172 82173*4021 = 330417633 1 173 82173*784 = 64423632 1 174 82173*625 = 51358125 1 175 82173*98 = 8052954 1 188 82173*784 = 64423632 1 189 82173*64 = 5259072 1 190 82173*64 = 5259072 1 191 82173*8 = 657384 1 232 82173*3071 = 252353283 1 233 82173*512 = 42072576 1 234 82173*625 = 51358125 1 235 82173*64 = 5259072 1 238 82173*98 = 8052954 1 239 82173*8 = 657384 1 254 82173*8 = 657384 1 255 82173*1 = 82173 22 22 20472*20472 = 419102784 3 61 51060*784 = 40031040 3 63 51060*98 = 5003880 3 86 51060*5000 = 255300000 3 87 51060*625 = 31912500 6 52 51052*25777 = 1315967404 6 53 51052*4021 = 205280092 5 58 51060*4021 = 205312260 6 55 51052*625 = 31907500 3 94 51060*784 = 40031040 3 95 51060*98 = 5003880 3 104 51060*20472 = 1045300320 3 105 51060*4825 = 246364500 6 58 51052*4021 = 205280092 3 107 51060*512 = 26142720 3 108 51060*5000 = 255300000 3 109 51060*512 = 26142720 6 62 51052*784 = 40024768 3 111 51060*64 = 3267840 3 124 51060*784 = 40031040 3 125 51060*64 = 3267840 3 126 51060*64 = 3267840 3 127 51060*8 = 408480 3 192 51060*51060 = 2607123600 12 49 51060*16836 = 859646160 12 51 51060*5750 = 293595000 3 197 51060*4021 = 205312260 3 198 51060*5000 = 255300000 12 55 51060*625 = 31912500 3 207 51060*98 = 5003880 3 212 51060*3071 = 156805260 3 213 51060*625 = 31912500 3 214 51060*512 = 26142720 3 215 51060*64 = 3267840 3 216 51060*4021 = 205312260 3 217 51060*784 = 40031040 3 219 51060*64 = 3267840 3 220 51060*625 = 31912500 3 221 51060*98 = 5003880 3 222 51060*64 = 3267840 3 223 51060*8 = 408480 3 252 51060*98 = 5003880 3 253 51060*8 = 408480 3 255 51060*1 = 51060 6 96 51052*51052 = 2606306704 6 97 51052*20472 = 1045136544 20 42 51052*16836 = 859511472 20 43 51052*3071 = 156780692 21 42 16836*16836 = 283450896 6 103 51052*784 = 40024768 6 105 51052*4825 = 246325900 6 107 51052*512 = 26138624 6 111 51052*64 = 3267328 6 114 51052*4021 = 205280092 6 115 51052*625 = 31907500 6 118 51052*784 = 40024768 6 119 51052*98 = 5003096 6 120 51052*5000 = 255260000 6 121 51052*512 = 26138624 6 122 51052*784 = 40024768 6 123 51052*64 = 3267328 6 126 51052*64 = 3267328 6 127 51052*8 = 408416 6 144 51052*51052 = 2606306704 9 97 51052*20472 = 1045136544 6 147 51052*5000 = 255260000 6 150 51052*4825 = 246325900 6 151 51052*512 = 26138624 6 159 51052*64 = 3267328 6 176 51052*16836 = 859511472 6 177 51052*4021 = 205280092 6 178 51052*3071 = 156780692 6 179 51052*625 = 31907500 6 180 51052*5000 = 255260000 6 181 51052*784 = 40024768 6 182 51052*512 = 26138624 6 183 51052*64 = 3267328 6 185 51052*784 = 40024768 6 187 51052*98 = 5003096 6 189 51052*64 = 3267328 6 191 51052*8 = 408416 6 240 51052*5750 = 293549000 6 241 51052*625 = 31907500 6 242 51052*625 = 31907500 6 243 51052*98 = 5003096 6 246 51052*64 = 3267328 6 247 51052*8 = 408416 6 249 51052*64 = 3267328 6 251 51052*8 = 408416 6 255 51052*1 = 51052 7 118 16836*784 = 13199424 7 119 16836*98 = 1649928 7 120 16836*5000 = 84180000 7 121 16836*512 = 8620032 7 122 16836*784 = 13199424 7 123 16836*64 = 1077504 7 126 16836*64 = 1077504 7 127 16836*8 = 134688 7 176 16836*16836 = 283450896 11 113 16836*3071 = 51703356 24 63 69868*98 = 6847064 11 116 16836*4021 = 67697556 11 117 16836*625 = 10522500 7 182 16836*512 = 8620032 7 183 16836*64 = 1077504 7 188 16836*784 = 13199424 7 189 16836*64 = 1077504 7 191 16836*8 = 134688 7 224 16836*16836 = 283450896 14 113 16836*3071 = 51703356 7 226 16836*4021 = 67697556 14 115 16836*625 = 10522500 7 230 16836*784 = 13199424 7 231 16836*64 = 1077504 7 233 16836*512 = 8620032 7 235 16836*64 = 1077504 7 239 16836*8 = 134688 7 240 16836*5750 = 96807000 7 241 16836*625 = 10522500 7 242 16836*625 = 10522500 7 243 16836*98 = 1649928 7 246 16836*64 = 1077504 7 247 16836*8 = 134688 7 248 16836*625 = 10522500 7 249 16836*64 = 1077504 7 250 16836*98 = 1649928 7 251 16836*8 = 134688 7 254 16836*8 = 134688 7 255 16836*1 = 16836 15 240 5750*5750 = 33062500 15 241 5750*625 = 3593750 15 243 5750*98 = 563500 15 246 5750*64 = 368000 15 247 5750*8 = 46000 15 255 5750*1 = 5750 22 104 20472*20472 = 419102784 22 105 20472*4825 = 98777400 23 104 3071*20472 = 62869512 22 107 20472*512 = 10481664 23 106 3071*5000 = 15355000 22 111 20472*64 = 1310208 22 126 20472*64 = 1310208 22 127 20472*8 = 163776 22 129 20472*69868 = 1430337696 24 99 69868*5000 = 349340000 22 134 20472*20472 = 419102784 24 103 69868*784 = 54776512 24 105 69868*4825 = 337113100 24 107 69868*512 = 35772416 24 110 69868*784 = 54776512 24 111 69868*64 = 4471552 22 150 20472*4825 = 98777400 22 151 20472*512 = 10481664 22 152 20472*25777 = 527706744 25 105 25777*4825 = 124374025 22 154 20472*5000 = 102360000 25 107 25777*512 = 13197824 22 158 20472*512 = 10481664 22 159 20472*64 = 1310208 22 169 20472*5000 = 102360000 22 171 20472*625 = 12795000 22 172 20472*4021 = 82317912 26 109 25777*512 = 13197824 22 174 20472*625 = 12795000 26 111 25777*64 = 1649728 22 188 20472*784 = 16050048 22 189 20472*64 = 1310208 22 190 20472*64 = 1310208 22 191 20472*8 = 163776 22 233 20472*512 = 10481664 22 234 20472*625 = 12795000 22 235 20472*64 = 1310208 22 238 20472*98 = 2006256 22 239 20472*8 = 163776 22 254 20472*8 = 163776 22 255 20472*1 = 20472 23 126 3071*64 = 196544 23 127 3071*8 = 24568 23 129 3071*69868 = 214564628 24 115 69868*625 = 43667500 24 119 69868*98 = 6847064 24 121 69868*512 = 35772416 24 123 69868*64 = 4471552 24 126 69868*64 = 4471552 24 127 69868*8 = 558944 23 150 3071*4825 = 14817575 23 151 3071*512 = 1572352 23 152 3071*25777 = 79161167 25 121 25777*512 = 13197824 23 154 3071*5000 = 15355000 25 123 25777*64 = 1649728 23 158 3071*512 = 1572352 23 159 3071*64 = 196544 26 121 25777*512 = 13197824 26 123 25777*64 = 1649728 23 172 3071*4021 = 12348491 26 125 25777*64 = 1649728 26 126 25777*64 = 1649728 26 127 25777*8 = 206216 23 188 3071*784 = 2407664 23 189 3071*64 = 196544 23 190 3071*64 = 196544 23 191 3071*8 = 24568 23 232 3071*3071 = 9431041 23 233 3071*512 = 1572352 23 234 3071*625 = 1919375 23 235 3071*64 = 196544 23 238 3071*98 = 300958 23 239 3071*8 = 24568 23 254 3071*8 = 24568 23 255 3071*1 = 3071 24 231 69868*64 = 4471552 24 239 69868*8 = 558944 24 255 69868*1 = 69868 25 225 25777*5000 = 128885000 25 227 25777*784 = 20209168 25 230 25777*784 = 20209168 25 231 25777*64 = 1649728 25 233 25777*512 = 13197824 25 234 25777*625 = 16110625 25 235 25777*64 = 1649728 25 238 25777*98 = 2526146 25 239 25777*8 = 206216 25 241 25777*625 = 16110625 25 243 25777*98 = 2526146 25 246 25777*64 = 1649728 25 247 25777*8 = 206216 25 248 25777*625 = 16110625 25 249 25777*64 = 1649728 47 92 625*4021 = 2513125 25 251 25777*8 = 206216 25 254 25777*8 = 206216 25 255 25777*1 = 25777 27 214 4021*512 = 2058752 27 215 4021*64 = 257344 27 216 4021*4021 = 16168441 46 117 4021*625 = 2513125 27 219 4021*64 = 257344 27 222 4021*64 = 257344 27 223 4021*8 = 32168 27 228 4021*4021 = 16168441 45 121 5000*512 = 2560000 27 231 4021*64 = 257344 27 236 4021*625 = 2513125 27 237 4021*64 = 257344 30 190 5000*64 = 320000 27 239 4021*8 = 32168 27 252 4021*98 = 394058 27 253 4021*8 = 32168 27 255 4021*1 = 4021 30 225 5000*5000 = 25000000 61 105 784*4825 = 3782800 30 230 5000*784 = 3920000 30 231 5000*64 = 320000 30 233 5000*512 = 2560000 30 235 5000*64 = 320000 30 238 5000*98 = 490000 30 239 5000*8 = 40000 30 241 5000*625 = 3125000 61 109 784*512 = 401408 30 246 5000*64 = 320000 30 247 5000*8 = 40000 30 249 5000*64 = 320000 31 234 625*625 = 390625 30 251 5000*8 = 40000 30 254 5000*8 = 40000 30 255 5000*1 = 5000 31 241 625*625 = 390625 31 242 625*625 = 390625 61 125 784*64 = 50176 31 246 625*64 = 40000 31 247 625*8 = 5000 31 248 625*625 = 390625 31 249 625*64 = 40000 62 126 784*64 = 50176 31 251 625*8 = 5000 31 254 625*8 = 5000 31 255 625*1 = 625 105 105 4825*4825 = 23280625 105 107 4825*512 = 2470400 107 107 512*512 = 262144 105 111 4825*64 = 308800 107 109 512*512 = 262144 107 111 512*64 = 32768 111 111 64*64 = 4096 105 126 4825*64 = 308800 105 127 4825*8 = 38600 62 214 784*512 = 401408 107 125 512*64 = 32768 107 126 512*64 = 32768 107 127 512*8 = 4096 61 237 784*64 = 50176 111 123 64*64 = 4096 61 253 784*8 = 6272 111 126 64*64 = 4096 111 127 64*8 = 512 126 126 64*64 = 4096 126 127 64*8 = 512 127 127 8*8 = 64 105 150 4825*4825 = 23280625 105 151 4825*512 = 2470400 107 151 512*512 = 262144 107 159 512*64 = 32768 111 159 64*64 = 4096 107 189 512*64 = 32768 107 191 512*8 = 4096 107 214 512*512 = 262144 107 215 512*64 = 32768 107 223 512*8 = 4096 107 253 512*8 = 4096 107 255 512*1 = 512 111 246 64*64 = 4096 111 247 64*8 = 512 111 249 64*64 = 4096 111 251 64*8 = 512 111 255 64*1 = 64 126 255 64*1 = 64 127 254 8*8 = 64 127 255 8*1 = 8 255 255 1*1 = 1
