Best Known (15, s)-Sequences in Base 9
(15, 63)-Sequence over F9 — Constructive and digital
Digital (15, 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
(15, 134)-Sequence in Base 9 — Upper bound on s
There is no (15, 135)-sequence in base 9, because
- net from sequence [i] would yield (15, m, 136)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (15, 123, 136)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9123, 136, S9, 108), but
- the linear programming bound shows that M ≥ 43937 926141 213657 416061 906681 876494 817263 274556 001188 989748 982782 114241 968389 523142 886351 436942 916837 719711 850478 384204 731164 785821 / 15 367369 428125 > 9123 [i]
- extracting embedded orthogonal array [i] would yield OA(9123, 136, S9, 108), but
- m-reduction [i] would yield (15, 123, 136)-net in base 9, but