Best Known (42−36, 42, s)-Nets in Base 81
(42−36, 42, 160)-Net over F81 — Constructive and digital
Digital (6, 42, 160)-net over F81, using
- t-expansion [i] based on digital (5, 42, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(42−36, 42, 190)-Net over F81 — Digital
Digital (6, 42, 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
(42−36, 42, 2671)-Net in Base 81 — Upper bound on s
There is no (6, 42, 2672)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 143 814529 460253 080272 578339 939908 464779 161941 690535 635135 313055 994975 235980 193281 > 8142 [i]