Best Known (8, s)-Sequences in Base 3
(8, 15)-Sequence over F3 — Constructive and digital
Digital (8, 15)-sequence over F3, using
- t-expansion [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
(8, 16)-Sequence over F3 — Digital
Digital (8, 16)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 8 and N(F) ≥ 17, using
(8, 23)-Sequence in Base 3 — Upper bound on s
There is no (8, 24)-sequence in base 3, because
- net from sequence [i] would yield (8, m, 25)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (8, 40, 25)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(340, 25, S3, 2, 32), but
- the linear programming bound for OOAs shows that M ≥ 1 208575 886414 878812 860993 894121 / 96985 358767 > 340 [i]
- extracting embedded OOA [i] would yield OOA(340, 25, S3, 2, 32), but
- m-reduction [i] would yield (8, 40, 25)-net in base 3, but