Best Known (75, 75+59, s)-Nets in Base 2
(75, 75+59, 50)-Net over F2 — Constructive and digital
Digital (75, 134, 50)-net over F2, using
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(75, 75+59, 54)-Net over F2 — Digital
Digital (75, 134, 54)-net over F2, using
(75, 75+59, 240)-Net in Base 2 — Upper bound on s
There is no (75, 134, 241)-net in base 2, because
- 1 times m-reduction [i] would yield (75, 133, 241)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 11918 538657 130234 579790 125621 517933 074576 > 2133 [i]