Best Known (47, 92, s)-Nets in Base 2
(47, 92, 34)-Net over F2 — Constructive and digital
Digital (47, 92, 34)-net over F2, using
- t-expansion [i] based on digital (45, 92, 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
(47, 92, 36)-Net over F2 — Digital
Digital (47, 92, 36)-net over F2, using
- net from sequence [i] based on digital (47, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 47 and N(F) ≥ 36, using
(47, 92, 110)-Net in Base 2 — Upper bound on s
There is no (47, 92, 111)-net in base 2, because
- 1 times m-reduction [i] would yield (47, 91, 111)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(291, 111, S2, 44), but
- the linear programming bound shows that M ≥ 4098 314390 537865 655038 841462 980608 / 1 584999 > 291 [i]
- extracting embedded orthogonal array [i] would yield OA(291, 111, S2, 44), but