Best Known (0, s)-Sequences in Base 9
(0, 9)-Sequence over F9 — Constructive and digital
Digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
(0, 9)-Sequence in Base 9 — Upper bound on s
There is no (0, 10)-sequence in base 9, because
- net from sequence [i] would yield (0, m, 11)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 11)-net in base 9, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 9m ≥ 89 > 92 [i]
- m-reduction [i] would yield (0, 2, 11)-net in base 9, but