Best Known (246−142, 246, s)-Nets in Base 2
(246−142, 246, 55)-Net over F2 — Constructive and digital
Digital (104, 246, 55)-net over F2, using
- t-expansion [i] based on digital (100, 246, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 6 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (100, 54)-sequence over F2, using
(246−142, 246, 65)-Net over F2 — Digital
Digital (104, 246, 65)-net over F2, using
- t-expansion [i] based on digital (95, 246, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(246−142, 246, 209)-Net in Base 2 — Upper bound on s
There is no (104, 246, 210)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 129 682711 526780 431373 125616 225021 219489 306655 922629 988349 583718 783096 783112 > 2246 [i]