Best Known (250−154, 250, s)-Nets in Base 2
(250−154, 250, 54)-Net over F2 — Constructive and digital
Digital (96, 250, 54)-net over F2, using
- t-expansion [i] based on digital (95, 250, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-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 5 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 (95, 53)-sequence over F2, using
(250−154, 250, 65)-Net over F2 — Digital
Digital (96, 250, 65)-net over F2, using
- t-expansion [i] based on digital (95, 250, 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
(250−154, 250, 182)-Net in Base 2 — Upper bound on s
There is no (96, 250, 183)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1978 247983 945576 823809 758063 314268 845766 811993 713237 551719 220487 748765 013744 > 2250 [i]