Best Known (256−164, 256, s)-Nets in Base 2
(256−164, 256, 53)-Net over F2 — Constructive and digital
Digital (92, 256, 53)-net over F2, using
- t-expansion [i] based on digital (90, 256, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-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 4 places 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]
- net from sequence [i] based on digital (90, 52)-sequence over F2, using
(256−164, 256, 60)-Net over F2 — Digital
Digital (92, 256, 60)-net over F2, using
- net from sequence [i] based on digital (92, 59)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 92 and N(F) ≥ 60, using
(256−164, 256, 170)-Net in Base 2 — Upper bound on s
There is no (92, 256, 171)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 126879 960979 045036 484549 333279 744526 046376 847085 643036 112270 176965 373934 346300 > 2256 [i]