Best Known (75, 75+134, s)-Nets in Base 2
(75, 75+134, 50)-Net over F2 — Constructive and digital
Digital (75, 209, 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+134, 140)-Net in Base 2 — Upper bound on s
There is no (75, 209, 141)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 919 018323 515625 581982 935423 058950 570705 568938 793611 515724 195328 > 2209 [i]