Best Known (94−42, 94, s)-Nets in Base 2
(94−42, 94, 36)-Net over F2 — Constructive and digital
Digital (52, 94, 36)-net over F2, using
- t-expansion [i] based on digital (51, 94, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-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 3 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 (51, 35)-sequence over F2, using
(94−42, 94, 40)-Net over F2 — Digital
Digital (52, 94, 40)-net over F2, using
- t-expansion [i] based on digital (50, 94, 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
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
(94−42, 94, 145)-Net in Base 2 — Upper bound on s
There is no (52, 94, 146)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(294, 146, S2, 42), but
- the linear programming bound shows that M ≥ 168 670907 663262 236513 872429 896360 338501 843579 568128 / 8247 290372 596431 535185 > 294 [i]