Best Known (45, 45+44, s)-Nets in Base 2
(45, 45+44, 34)-Net over F2 — Constructive and digital
Digital (45, 89, 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+44, 101)-Net over F2 — Upper bound on s (digital)
There is no digital (45, 89, 102)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(289, 102, F2, 44) (dual of [102, 13, 45]-code), but
(45, 45+44, 103)-Net in Base 2 — Upper bound on s
There is no (45, 89, 104)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(289, 104, S2, 44), but
- the linear programming bound shows that M ≥ 8 160500 738969 226772 135026 884608 / 12903 > 289 [i]