Best Known (56−42, 56, s)-Nets in Base 81
(56−42, 56, 224)-Net over F81 — Constructive and digital
Digital (14, 56, 224)-net over F81, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(56−42, 56, 298)-Net over F81 — Digital
Digital (14, 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
(56−42, 56, 13315)-Net in Base 81 — Upper bound on s
There is no (14, 56, 13316)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 75062 042113 744048 952889 520598 218458 571081 817882 682866 812004 291174 808697 017858 929332 376007 672510 965791 714881 > 8156 [i]