Best Known (33−20, 33, s)-Nets in Base 81
(33−20, 33, 224)-Net over F81 — Constructive and digital
Digital (13, 33, 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
(33−20, 33, 298)-Net over F81 — Digital
Digital (13, 33, 298)-net over F81, using
- t-expansion [i] based on digital (12, 33, 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
(33−20, 33, 112426)-Net in Base 81 — Upper bound on s
There is no (13, 33, 112427)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 955 040331 071318 708043 918771 981154 180033 036561 795760 311990 165601 > 8133 [i]