Best Known (0, s)-Sequences in Base 27
(0, 27)-Sequence over F27 — Constructive and digital
Digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
(0, 27)-Sequence in Base 27 — Upper bound on s
There is no (0, 28)-sequence in base 27, because
- net from sequence [i] would yield (0, m, 29)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 29)-net in base 27, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 27m ≥ 755 > 272 [i]
- m-reduction [i] would yield (0, 2, 29)-net in base 27, but