Best Known (41−33, 41, s)-Nets in Base 81
(41−33, 41, 172)-Net over F81 — Constructive and digital
Digital (8, 41, 172)-net over F81, using
- t-expansion [i] based on digital (7, 41, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(41−33, 41, 226)-Net over F81 — Digital
Digital (8, 41, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
(41−33, 41, 5011)-Net in Base 81 — Upper bound on s
There is no (8, 41, 5012)-net in base 81, because
- 1 times m-reduction [i] would yield (8, 40, 5012)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 21860 548262 145212 566868 128950 723124 088251 869240 984377 825459 538876 314275 599361 > 8140 [i]