Best Known (50, 90, s)-Nets in Base 2
(50, 90, 35)-Net over F2 — Constructive and digital
Digital (50, 90, 35)-net over F2, using
- t-expansion [i] based on digital (48, 90, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
(50, 90, 40)-Net over F2 — Digital
Digital (50, 90, 40)-net over F2, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 50 and N(F) ≥ 40, using
(50, 90, 142)-Net in Base 2 — Upper bound on s
There is no (50, 90, 143)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(290, 143, S2, 40), but
- the linear programming bound shows that M ≥ 317300 634780 115553 893444 812307 057689 267816 890368 / 255 074823 257151 213225 > 290 [i]