Best Known (51−38, 51, s)-Nets in Base 81
(51−38, 51, 224)-Net over F81 — Constructive and digital
Digital (13, 51, 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
(51−38, 51, 298)-Net over F81 — Digital
Digital (13, 51, 298)-net over F81, using
- t-expansion [i] based on digital (12, 51, 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
(51−38, 51, 13140)-Net in Base 81 — Upper bound on s
There is no (13, 51, 13141)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 21 545304 964209 227961 226715 455396 545033 710095 932211 229745 680789 066571 337627 445087 036130 338599 820721 > 8151 [i]