Best Known (0, ∞, s)-Nets in Base 8
(0, ∞, 9)-Net over F8 — Constructive and digital
Digital (0, m, 9)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
(0, ∞, 9)-Net in Base 8 — Upper bound on s
There is no (0, m, 10)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (0, 2, 10)-net in base 8, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 8m ≥ 71 > 82 [i]