MinT - Best Known (52−29, 52, s)-Nets in Base 256

Best Known (52−29, 52, s)-Nets in Base 256

(52−29, 52, 771)-Net over F₂₅₆ — Constructive and digital

Digital (23, 52, 771)-net over F₂₅₆, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 9, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]
2. digital (0, 14, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
3. digital (0, 29, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(52−29, 52, 1329)-Net over F₂₅₆ — Digital

Digital (23, 52, 1329)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(52−29, 52, large)-Net in Base 256 — Upper bound on s

There is no (23, 52, large)-net in base 256, because

27 times m-reduction [i] would yield (23, 25, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]