Best Known (54−41, 54, s)-Nets in Base 81
(54−41, 54, 224)-Net over F81 — Constructive and digital
Digital (13, 54, 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
(54−41, 54, 298)-Net over F81 — Digital
Digital (13, 54, 298)-net over F81, using
- t-expansion [i] based on digital (12, 54, 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
(54−41, 54, 11839)-Net in Base 81 — Upper bound on s
There is no (13, 54, 11840)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 53, 11840)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 141207 480530 234719 721304 152917 065072 877138 271662 881837 172662 154637 443433 746169 338202 744634 517758 464001 > 8153 [i]