Best Known (30, s)-Sequences in Base 7
(30, 32)-Sequence over F7 — Constructive and digital
Digital (30, 32)-sequence over F7, using
- t-expansion [i] based on digital (29, 32)-sequence over F7, using
(30, 77)-Sequence over F7 — Digital
Digital (30, 77)-sequence over F7, using
- t-expansion [i] based on 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
(30, 199)-Sequence in Base 7 — Upper bound on s
There is no (30, 200)-sequence in base 7, because
- net from sequence [i] would yield (30, m, 201)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (30, 599, 201)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7599, 201, S7, 3, 569), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26336 123164 313581 047236 355744 009340 500833 497588 753881 869878 225764 658754 133752 559919 230862 548925 022419 887639 059565 515557 682494 942752 358833 788703 178836 933671 548358 993800 827590 817556 047150 695384 545006 253962 531540 143018 679662 044626 439346 248348 686377 167623 853396 152776 468726 094851 866009 018738 037260 693847 682625 119389 527365 825847 918873 741092 465334 185044 783951 758094 291273 526764 158745 177532 729560 021351 401559 057372 076945 333704 945139 358652 888691 184971 973508 293149 252904 938676 504970 171376 548414 656547 822090 338072 280023 / 95 > 7599 [i]
- extracting embedded OOA [i] would yield OOA(7599, 201, S7, 3, 569), but
- m-reduction [i] would yield (30, 599, 201)-net in base 7, but