Best Known (256−144, 256, s)-Nets in Base 2
(256−144, 256, 57)-Net over F2 — Constructive and digital
Digital (112, 256, 57)-net over F2, using
- t-expansion [i] based on digital (110, 256, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(256−144, 256, 72)-Net over F2 — Digital
Digital (112, 256, 72)-net over F2, using
- t-expansion [i] based on digital (110, 256, 72)-net over F2, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 110 and N(F) ≥ 72, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
(256−144, 256, 231)-Net in Base 2 — Upper bound on s
There is no (112, 256, 232)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 136316 942595 523359 651280 708816 955373 672861 576444 103880 223395 295579 488854 031924 > 2256 [i]