Best Known (80, 80+28, s)-Nets in Base 2
(80, 80+28, 105)-Net over F2 — Constructive and digital
Digital (80, 108, 105)-net over F2, using
- trace code for nets [i] based on digital (8, 36, 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
(80, 80+28, 156)-Net over F2 — Digital
Digital (80, 108, 156)-net over F2, using
(80, 80+28, 1249)-Net in Base 2 — Upper bound on s
There is no (80, 108, 1250)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 326 984471 861973 087979 311769 239376 > 2108 [i]