Best Known (7, 7+42, s)-Nets in Base 81
(7, 7+42, 172)-Net over F81 — Constructive and digital
Digital (7, 49, 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
(7, 7+42, 190)-Net over F81 — Digital
Digital (7, 49, 190)-net over F81, using
- t-expansion [i] based on digital (6, 49, 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
(7, 7+42, 3069)-Net in Base 81 — Upper bound on s
There is no (7, 49, 3070)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3287 516528 324752 228909 482034 741225 665212 961503 330875 272371 139967 682704 003412 172446 228388 197601 > 8149 [i]