Best Known (50−40, 50, s)-Nets in Base 81
(50−40, 50, 172)-Net over F81 — Constructive and digital
Digital (10, 50, 172)-net over F81, using
- t-expansion [i] based on digital (7, 50, 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
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(50−40, 50, 244)-Net over F81 — Digital
Digital (10, 50, 244)-net over F81, using
- t-expansion [i] based on digital (9, 50, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
(50−40, 50, 6119)-Net in Base 81 — Upper bound on s
There is no (10, 50, 6120)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 265782 248166 120696 381646 434606 447261 124060 508989 616349 313631 730813 721361 578530 250536 274117 952001 > 8150 [i]