Best Known (86−40, 86, s)-Nets in Base 2
(86−40, 86, 34)-Net over F2 — Constructive and digital
Digital (46, 86, 34)-net over F2, using
- t-expansion [i] based on digital (45, 86, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-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 1 place 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 (45, 33)-sequence over F2, using
(86−40, 86, 116)-Net in Base 2 — Upper bound on s
There is no (46, 86, 117)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(286, 117, S2, 40), but
- the linear programming bound shows that M ≥ 130542 530684 708997 729272 044030 263296 / 1503 240375 > 286 [i]