Best Known (35, s)-Sequences in Base 3
(35, 37)-Sequence over F3 — Constructive and digital
Digital (35, 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
(35, 46)-Sequence over F3 — Digital
Digital (35, 46)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 35 and N(F) ≥ 47, using
(35, 80)-Sequence in Base 3 — Upper bound on s
There is no (35, 81)-sequence in base 3, because
- net from sequence [i] would yield (35, m, 82)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (35, 322, 82)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3322, 82, S3, 4, 287), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 21478 998321 508685 151891 532661 152398 311230 118386 765733 123253 852366 559739 409623 256380 662504 746040 817020 833978 322267 663353 316788 705688 003932 660075 517428 768045 / 4 > 3322 [i]
- extracting embedded OOA [i] would yield OOA(3322, 82, S3, 4, 287), but
- m-reduction [i] would yield (35, 322, 82)-net in base 3, but