Best Known (76, 76+25, s)-Nets in Base 2
(76, 76+25, 105)-Net over F2 — Constructive and digital
Digital (76, 101, 105)-net over F2, using
- 1 times m-reduction [i] based on digital (76, 102, 105)-net over F2, using
- trace code for nets [i] based on digital (8, 34, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- trace code for nets [i] based on digital (8, 34, 35)-net over F8, using
(76, 76+25, 167)-Net over F2 — Digital
Digital (76, 101, 167)-net over F2, using
(76, 76+25, 1688)-Net in Base 2 — Upper bound on s
There is no (76, 101, 1689)-net in base 2, because
- 1 times m-reduction [i] would yield (76, 100, 1689)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 272603 206575 617602 987783 182092 > 2100 [i]