Best Known (45, 45+48, s)-Nets in Base 2
(45, 45+48, 34)-Net over F2 — Constructive and digital
Digital (45, 93, 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]
(45, 45+48, 98)-Net over F2 — Upper bound on s (digital)
There is no digital (45, 93, 99)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(293, 99, F2, 48) (dual of [99, 6, 49]-code), but
(45, 45+48, 101)-Net in Base 2 — Upper bound on s
There is no (45, 93, 102)-net in base 2, because
- 2 times m-reduction [i] would yield (45, 91, 102)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(291, 102, S2, 46), but
- the linear programming bound shows that M ≥ 1 356782 283056 776781 289440 149504 / 435 > 291 [i]
- extracting embedded orthogonal array [i] would yield OA(291, 102, S2, 46), but