Best Known (27, s)-Sequences in Base 7
(27, 31)-Sequence over F7 — Constructive and digital
Digital (27, 31)-sequence over F7, using
(27, 77)-Sequence over F7 — Digital
Digital (27, 77)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 27 and N(F) ≥ 78, using
(27, 180)-Sequence in Base 7 — Upper bound on s
There is no (27, 181)-sequence in base 7, because
- net from sequence [i] would yield (27, m, 182)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (27, 542, 182)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7542, 182, S7, 3, 515), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5411 700678 756365 696824 025595 934470 196097 258050 066998 606063 328244 970222 550532 535670 483050 563185 009319 592109 323887 966577 657652 272196 940297 143064 578368 620270 284969 871224 353638 754151 502423 344306 032534 295152 094069 146288 780018 574837 440950 610555 559388 062060 373960 685148 901556 438209 232137 902359 428722 221267 946233 941335 683621 390277 220198 720303 133494 508972 368474 785218 097174 183697 472110 851484 828993 559415 154051 519736 541562 198468 612041 784523 600359 188478 380797 533837 126401 / 43 > 7542 [i]
- extracting embedded OOA [i] would yield OOA(7542, 182, S7, 3, 515), but
- m-reduction [i] would yield (27, 542, 182)-net in base 7, but