Best Known (42−38, 42, s)-Nets in Base 81
(42−38, 42, 150)-Net over F81 — Constructive and digital
Digital (4, 42, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
(42−38, 42, 154)-Net over F81 — Digital
Digital (4, 42, 154)-net over F81, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
(42−38, 42, 1630)-Net in Base 81 — Upper bound on s
There is no (4, 42, 1631)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 143 479716 128233 613153 780791 538718 057302 111655 093520 942792 322878 628309 419283 989521 > 8142 [i]