Best Known (32, s)-Sequences in Base 3
(32, 37)-Sequence over F3 — Constructive and digital
Digital (32, 37)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 32 and N(F) ≥ 38, using
(32, 41)-Sequence over F3 — Digital
Digital (32, 41)-sequence over F3, using
- t-expansion [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
(32, 74)-Sequence in Base 3 — Upper bound on s
There is no (32, 75)-sequence in base 3, because
- net from sequence [i] would yield (32, m, 76)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (32, 298, 76)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3298, 76, S3, 4, 266), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 962111 199839 766722 542339 725809 932528 852646 303963 169922 757882 724456 622292 877486 764511 136288 231541 493231 590276 981904 581280 327015 836308 306102 112681 / 89 > 3298 [i]
- extracting embedded OOA [i] would yield OOA(3298, 76, S3, 4, 266), but
- m-reduction [i] would yield (32, 298, 76)-net in base 3, but