Best Known (42−42, 42, s)-Nets in Base 4
(42−42, 42, 5)-Net over F4 — Constructive and digital
Digital (0, 42, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
(42−42, 42, 5)-Net in Base 4 — Upper bound on s
There is no (0, 42, 6)-net in base 4, because
- 40 times m-reduction [i] would yield (0, 2, 6)-net in base 4, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 4m ≥ 19 > 42 [i]