Best Known (99−46, 99, s)-Nets in Base 2
(99−46, 99, 36)-Net over F2 — Constructive and digital
Digital (53, 99, 36)-net over F2, using
- t-expansion [i] based on digital (51, 99, 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
(99−46, 99, 40)-Net over F2 — Digital
Digital (53, 99, 40)-net over F2, using
- t-expansion [i] based on digital (50, 99, 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
(99−46, 99, 130)-Net in Base 2 — Upper bound on s
There is no (53, 99, 131)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(299, 131, S2, 46), but
- the linear programming bound shows that M ≥ 306 212137 528001 216698 591406 299528 822784 / 435 599073 > 299 [i]