Best Known (4, 4+31, s)-Nets in Base 81
(4, 4+31, 150)-Net over F81 — Constructive and digital
Digital (4, 35, 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
(4, 4+31, 154)-Net over F81 — Digital
Digital (4, 35, 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
(4, 4+31, 1693)-Net in Base 81 — Upper bound on s
There is no (4, 35, 1694)-net in base 81, because
- 1 times m-reduction [i] would yield (4, 34, 1694)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 77823 175005 909543 962599 257260 044749 559997 572934 911705 491207 312801 > 8134 [i]