Best Known (40, 40+58, s)-Nets in Base 3
(40, 40+58, 42)-Net over F3 — Constructive and digital
Digital (40, 98, 42)-net over F3, using
- t-expansion [i] based on digital (39, 98, 42)-net over F3, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
(40, 40+58, 56)-Net over F3 — Digital
Digital (40, 98, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
(40, 40+58, 211)-Net in Base 3 — Upper bound on s
There is no (40, 98, 212)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 58297 004649 525868 880724 379736 662528 282427 898633 > 398 [i]