Best Known (49, 49+41, s)-Nets in Base 2
(49, 49+41, 35)-Net over F2 — Constructive and digital
Digital (49, 90, 35)-net over F2, using
- t-expansion [i] based on digital (48, 90, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-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 2 places 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 (48, 34)-sequence over F2, using
(49, 49+41, 37)-Net over F2 — Digital
Digital (49, 90, 37)-net over F2, using
(49, 49+41, 136)-Net in Base 2 — Upper bound on s
There is no (49, 90, 137)-net in base 2, because
- 1 times m-reduction [i] would yield (49, 89, 137)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(289, 137, S2, 40), but
- the linear programming bound shows that M ≥ 94 055793 389946 937848 891499 500557 263777 562624 / 137978 313328 366875 > 289 [i]
- extracting embedded orthogonal array [i] would yield OA(289, 137, S2, 40), but