MinT - Best Known (11, 34, s)-Nets in Base 256

Best Known (11, 34, s)-Nets in Base 256

(11, 34, 514)-Net over F₂₅₆ — Constructive and digital

Digital (11, 34, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 11, 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, 23, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(11, 34, 322988)-Net in Base 256 — Upper bound on s

There is no (11, 34, 322989)-net in base 256, because

1 times m-reduction [i] would yield (11, 33, 322989)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 29 643256 234891 299296 638377 890511 366187 751427 521336 847513 180966 501813 586570 675396 > 256³³ [i]