Best Known (0, s)-Sequences in Base 81
(0, 81)-Sequence over F81 — Constructive and digital
Digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
(0, 81)-Sequence in Base 81 — Upper bound on s
There is no (0, 82)-sequence in base 81, because
- net from sequence [i] would yield (0, m, 83)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 83)-net in base 81, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 81m ≥ 6641 > 812 [i]
- m-reduction [i] would yield (0, 2, 83)-net in base 81, but