Canou family: Difference between revisions

Sort by strong/weak extension
+19-limit extensions to semicanou, and misc cleanup
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POTE generators: ~3/2 = 702.1807, ~81/70 = 254.6239
POTE generators: ~3/2 = 702.1807, ~81/70 = 254.6239


Vals: {{Val list| 94, 118f, 193f, 212, 217, 311, 740, 1051d }}
Optimal GPV sequence: {{val list| 94, 118f, 193f, 212, 217, 311, 740, 1051d }}


Badness: 2.555 × 10<sup>-3</sup>
Badness: 2.555 × 10<sup>-3</sup>
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POTE generators: ~3/2 = 703.8423, ~15/13 = 254.3605
POTE generators: ~3/2 = 703.8423, ~15/13 = 254.3605


Vals: {{Val list| 75ef, 80, 99e, 104c, 179e, 184c, 203ce }}
Optimal GPV sequence: {{val list| 75ef, 80, 99e, 104c, 179e, 184c, 203ce }}


Badness: 3.470 × 10<sup>-3</sup>
Badness: 3.470 × 10<sup>-3</sup>
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POTE generators: ~3/2 = 703.8695, ~64/55 = 254.6321
POTE generators: ~3/2 = 703.8695, ~64/55 = 254.6321


Vals: {{Val list| 75e, 80, 99ef, 179ef }}
Optimal GPV sequence: {{val list| 75e, 80, 99ef, 179ef }}


Badness: 4.781 × 10<sup>-3</sup>
Badness: 4.781 × 10<sup>-3</sup>
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Mapping generators: ~99/70, ~3, ~81/70
Mapping generators: ~99/70, ~3, ~81/70


[[POTE generator]]s: ~3/2 = 702.3850, ~81/70 = 254.6168 or ~11/9 = 345.3832
[[POTE generator]]s: ~3/2 = 702.3850, ~81/70 = 254.6168


{{Val list|legend=1| 80, 94, 118, 198, 212, 292, 330e, 410 }}
{{Val list|legend=1| 80, 94, 118, 198, 212, 292, 330e, 410 }}
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Mapping: [{{val| 2 0 0 -2 1 -11 }}, {{val| 0 1 2 2 2 5 }}, {{val| 0 0 -4 3 -1 6 }}]
Mapping: [{{val| 2 0 0 -2 1 -11 }}, {{val| 0 1 2 2 2 5 }}, {{val| 0 0 -4 3 -1 6 }}]


POTE generators: ~3/2 = 702.5046, ~81/70 = 254.6501 or ~11/9 = 345.3499
POTE generators: ~3/2 = 702.5046, ~81/70 = 254.6501


Vals: {{Val list| 80f, 94, 118f, 198, 410 }}
Optimal GPV sequence: {{val list| 80f, 94, 118f, 198, 410 }}


Badness: 2.974 × 10<sup>-3</sup>
Badness: 2.974 × 10<sup>-3</sup>
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 1089/1088, 1225/1224, 14641/14580
Mapping: [{{val| 2 0 0 -2 1 -11 -10 }}, {{val| 0 1 2 2 2 5 6 }}, {{val| 0 0 -4 3 -1 6 -2 }}]
POTE generators: ~3/2 = 702.4241, ~81/70 = 254.6672
Optimal GPV sequence: {{val list| 94, 118f, 198g, 212g, 292, 410 }}
Badness: 2.421 × 10<sup>-3</sup>
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 715/714, 1089/1088, 1216/1215, 1225/1224, 1445/1444
Mapping: [{{val| 2 0 0 -2 1 -11 -10 -12 }}, {{val| 0 1 2 2 2 5 6 7 }}, {{val| 0 0 -4 3 -1 6 -2 -4 }}]
POTE generators: ~3/2 = 702.3551, ~81/70 = 254.6866
Optimal GPV sequence: {{val list| 94, 118f, 198gh, 212gh, 292h, 410, 622ef }}
Badness: 2.177 × 10<sup>-3</sup>


=== Semicanoumint ===
=== Semicanoumint ===
Line 155: Line 181:
POTE generators: ~3/2 = 702.8788, ~81/70 = 254.6664 or ~11/9 = 345.3336
POTE generators: ~3/2 = 702.8788, ~81/70 = 254.6664 or ~11/9 = 345.3336


Vals: {{Val list| 80, 94, 118, 174d, 198, 490f }}
Optimal GPV sequence: {{val list| 80, 94, 118, 174d, 198, 490f }}


Badness: 2.701 × 10<sup>-3</sup>
Badness: 2.701 × 10<sup>-3</sup>
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POTE generators: ~3/2 = 702.7876, ~15/13 = 254.3411 or ~11/9 = 345.6789
POTE generators: ~3/2 = 702.7876, ~15/13 = 254.3411 or ~11/9 = 345.6789


Vals: {{Val list| 80, 104c, 118f, 198f, 420cff }}
Optimal GPV sequence: {{val list| 80, 104c, 118f, 198f, 420cff }}


Badness: 3.511 × 10<sup>-3</sup>
Badness: 3.511 × 10<sup>-3</sup>