Best Known (41, 252, s)-Nets in Base 2
(41, 252, 33)-Net over F2 — Constructive and digital
Digital (41, 252, 33)-net over F2, using
- t-expansion [i] based on digital (39, 252, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(41, 252, 50)-Net in Base 2 — Upper bound on s
There is no (41, 252, 51)-net in base 2, because
- 7 times m-reduction [i] would yield (41, 245, 51)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2245, 51, S2, 5, 204), but
- the LP bound with quadratic polynomials shows that M ≥ 62532 251316 636578 192612 065146 293372 112166 310078 221906 165839 886676 148399 112192 / 1025 > 2245 [i]
- extracting embedded OOA [i] would yield OOA(2245, 51, S2, 5, 204), but