Best Known (14, s)-Sequences in Base 9
(14, 63)-Sequence over F9 — Constructive and digital
Digital (14, 63)-sequence over F9, using
- t-expansion [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
(14, 126)-Sequence in Base 9 — Upper bound on s
There is no (14, 127)-sequence in base 9, because
- net from sequence [i] would yield (14, m, 128)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (14, 115, 128)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9115, 128, S9, 101), but
- the linear programming bound shows that M ≥ 443 166910 356198 778018 116730 424202 752086 605368 053990 969284 924273 837502 116929 265381 334877 312358 520249 430979 777899 498996 052429 / 7 631616 168397 > 9115 [i]
- extracting embedded orthogonal array [i] would yield OA(9115, 128, S9, 101), but
- m-reduction [i] would yield (14, 115, 128)-net in base 9, but