Best Known (0, s)-Sequences in Base 25
(0, 25)-Sequence over F25 — Constructive and digital
Digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
(0, 25)-Sequence in Base 25 — Upper bound on s
There is no (0, 26)-sequence in base 25, because
- net from sequence [i] would yield (0, m, 27)-net in base 25 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 27)-net in base 25, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 25m ≥ 649 > 252 [i]
- m-reduction [i] would yield (0, 2, 27)-net in base 25, but