Best Known (58−45, 58, s)-Nets in Base 81
(58−45, 58, 224)-Net over F81 — Constructive and digital
Digital (13, 58, 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
(58−45, 58, 298)-Net over F81 — Digital
Digital (13, 58, 298)-net over F81, using
- t-expansion [i] based on digital (12, 58, 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
(58−45, 58, 9954)-Net in Base 81 — Upper bound on s
There is no (13, 58, 9955)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 57, 9955)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 6 087719 240687 246299 514299 435895 800455 132445 629654 268889 223093 226584 667791 648518 083092 251246 907379 474409 136801 > 8157 [i]