Best Known (47−40, 47, s)-Nets in Base 81
(47−40, 47, 172)-Net over F81 — Constructive and digital
Digital (7, 47, 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
(47−40, 47, 190)-Net over F81 — Digital
Digital (7, 47, 190)-net over F81, using
- t-expansion [i] based on digital (6, 47, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(47−40, 47, 3160)-Net in Base 81 — Upper bound on s
There is no (7, 47, 3161)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 499917 924562 132152 468001 023497 433409 124176 626296 122294 700667 594171 499577 690984 218168 193601 > 8147 [i]