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][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