Best Known (40, 40+75, s)-Nets in Base 2
(40, 40+75, 33)-Net over F2 — Constructive and digital
Digital (40, 115, 33)-net over F2, using
- t-expansion [i] based on digital (39, 115, 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
(40, 40+75, 78)-Net in Base 2 — Upper bound on s
There is no (40, 115, 79)-net in base 2, because
- 1 times m-reduction [i] would yield (40, 114, 79)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 27929 859466 579124 627600 057286 255560 > 2114 [i]