Best Known (42, 75, s)-Nets in Base 2
(42, 75, 33)-Net over F2 — Constructive and digital
Digital (42, 75, 33)-net over F2, using
- t-expansion [i] based on digital (39, 75, 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
(42, 75, 35)-Net over F2 — Digital
Digital (42, 75, 35)-net over F2, using
(42, 75, 145)-Net in Base 2 — Upper bound on s
There is no (42, 75, 146)-net in base 2, because
- 1 times m-reduction [i] would yield (42, 74, 146)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 19456 495213 635376 951977 > 274 [i]
- extracting embedded orthogonal array [i] would yield OA(274, 146, S2, 32), but
- the linear programming bound shows that M ≥ 280 270393 355737 497844 513648 098820 271740 172522 302191 747635 045255 952555 211698 995200 / 14596 329528 207009 222060 595527 173338 787771 222351 404958 268831 > 274 [i]