Best Known (30, s)-Sequences in Base 8
(30, 64)-Sequence over F8 — Constructive and digital
Digital (30, 64)-sequence over F8, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
(30, 96)-Sequence over F8 — Digital
Digital (30, 96)-sequence over F8, using
- t-expansion [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
(30, 231)-Sequence in Base 8 — Upper bound on s
There is no (30, 232)-sequence in base 8, because
- net from sequence [i] would yield (30, m, 233)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (30, 695, 233)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8695, 233, S8, 3, 665), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 007610 203192 743280 992870 720797 651784 589290 399498 477461 803204 517210 287759 645196 809361 656014 125747 513545 403823 333758 906169 485923 674595 642044 756502 226337 939128 912102 893232 500794 145135 790791 496314 530846 983621 213924 829689 199487 856469 783818 312719 701903 801734 529048 403910 185410 389477 382940 420845 019559 983530 120501 516059 739406 860558 479484 517227 183730 882316 331695 877224 166023 351823 432146 578643 465015 319664 070565 379142 491362 318894 473801 151502 613657 666780 718290 338588 807101 294914 957865 260485 381876 663263 086414 427091 215929 075920 315044 375274 128743 108815 041081 852052 207158 800627 145027 543760 384478 412510 746285 490978 460237 015689 995834 926945 009664 / 333 > 8695 [i]
- extracting embedded OOA [i] would yield OOA(8695, 233, S8, 3, 665), but
- m-reduction [i] would yield (30, 695, 233)-net in base 8, but