Best Known (4, 4+52, s)-Nets in Base 81
(4, 4+52, 150)-Net over F81 — Constructive and digital
Digital (4, 56, 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+52, 154)-Net over F81 — Digital
Digital (4, 56, 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+52, 1630)-Net in Base 81 — Upper bound on s
There is no (4, 56, 1631)-net in base 81, because
- 12 times m-reduction [i] would yield (4, 44, 1631)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 947244 322171 630230 231456 502483 163695 747478 661873 932985 789411 059049 810416 493323 825601 > 8144 [i]