Best Known (10, s)-Sequences in Base 3
(10, 18)-Sequence over F3 — Constructive and digital
Digital (10, 18)-sequence over F3, using
- t-expansion [i] based on digital (9, 18)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using
(10, 19)-Sequence over F3 — Digital
Digital (10, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 10 and N(F) ≥ 20, using
(10, 27)-Sequence in Base 3 — Upper bound on s
There is no (10, 28)-sequence in base 3, because
- net from sequence [i] would yield (10, m, 29)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (10, 83, 29)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(383, 29, S3, 3, 73), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 155642 697373 306257 251835 620347 321612 373853 / 37 > 383 [i]
- extracting embedded OOA [i] would yield OOA(383, 29, S3, 3, 73), but
- m-reduction [i] would yield (10, 83, 29)-net in base 3, but