Best Known (0, 0+∞, s)-Nets in Base 3
(0, 0+∞, 4)-Net over F3 — Constructive and digital
Digital (0, m, 4)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
(0, 0+∞, 4)-Net in Base 3 — Upper bound on s
There is no (0, m, 5)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (0, 2, 5)-net in base 3, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 3m ≥ 11 > 32 [i]