Best Known (36, s)-Sequences in Base 3
(36, 37)-Sequence over F3 — Constructive and digital
Digital (36, 37)-sequence over F3, using
- t-expansion [i] based on 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
(36, 47)-Sequence over F3 — Digital
Digital (36, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 36 and N(F) ≥ 48, using
(36, 82)-Sequence in Base 3 — Upper bound on s
There is no (36, 83)-sequence in base 3, because
- net from sequence [i] would yield (36, m, 84)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (36, 330, 84)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3330, 84, S3, 4, 294), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9892 844300 716777 526365 536274 445426 149462 652632 837012 246521 130481 465291 208710 980594 969573 893441 920793 253159 570422 349376 130023 839000 933364 913229 433983 480329 455799 / 295 > 3330 [i]
- extracting embedded OOA [i] would yield OOA(3330, 84, S3, 4, 294), but
- m-reduction [i] would yield (36, 330, 84)-net in base 3, but