Best Known (86−41, 86, s)-Nets in Base 2
(86−41, 86, 34)-Net over F2 — Constructive and digital
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]
(86−41, 86, 111)-Net in Base 2 — Upper bound on s
There is no (45, 86, 112)-net in base 2, because
- 1 times m-reduction [i] would yield (45, 85, 112)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(285, 112, S2, 40), but
- the linear programming bound shows that M ≥ 155 688291 100686 564892 413458 907136 / 3 717945 > 285 [i]
- extracting embedded orthogonal array [i] would yield OA(285, 112, S2, 40), but