Best Known (85−38, 85, s)-Nets in Base 2
(85−38, 85, 34)-Net over F2 — Constructive and digital
Digital (47, 85, 34)-net over F2, using
- t-expansion [i] based on digital (45, 85, 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
(85−38, 85, 37)-Net over F2 — Digital
Digital (47, 85, 37)-net over F2, using
(85−38, 85, 135)-Net in Base 2 — Upper bound on s
There is no (47, 85, 136)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(285, 136, S2, 38), but
- the linear programming bound shows that M ≥ 281878 418715 942127 522501 886591 136557 699958 833152 / 6656 924618 213909 378625 > 285 [i]