Best Known (0, s)-Sequences in Base 5
(0, 5)-Sequence over F5 — Constructive and digital
Digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
(0, 5)-Sequence in Base 5 — Upper bound on s
There is no (0, 6)-sequence in base 5, because
- net from sequence [i] would yield (0, m, 7)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 7)-net in base 5, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 5m ≥ 29 > 52 [i]
- m-reduction [i] would yield (0, 2, 7)-net in base 5, but