Best Known (56−43, 56, s)-Nets in Base 81
(56−43, 56, 224)-Net over F81 — Constructive and digital
Digital (13, 56, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
(56−43, 56, 298)-Net over F81 — Digital
Digital (13, 56, 298)-net over F81, using
- t-expansion [i] based on digital (12, 56, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(56−43, 56, 10799)-Net in Base 81 — Upper bound on s
There is no (13, 56, 10800)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 55, 10800)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 927 054387 300781 280334 225825 842917 822582 597765 227103 345694 952493 594218 362642 004794 214985 355107 956843 744001 > 8155 [i]