Best Known (0, 0+∞, s)-Nets in Base 2
(0, 0+∞, 3)-Net over F2 — Constructive and digital
Digital (0, m, 3)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 0 and N(F) ≥ 3, using
- the rational function field F2(x) [i]
- Niederreiter sequence [i]
- Sobol sequence [i]
(0, 0+∞, 3)-Net in Base 2 — Upper bound on s
There is no (0, m, 4)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (0, 2, 4)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 5 > 22 [i]