MinT - Best Known (46−31, 46, s)-Nets in Base 256

Best Known (46−31, 46, s)-Nets in Base 256

(46−31, 46, 514)-Net over F₂₅₆ — Constructive and digital

Digital (15, 46, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 15, 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, 31, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(46−31, 46, 422609)-Net in Base 256 — Upper bound on s

There is no (15, 46, 422610)-net in base 256, because

1 times m-reduction [i] would yield (15, 45, 422610)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 348596 686232 787457 071259 686394 669234 338797 963358 047823 914902 898956 897049 333254 421597 519759 762668 981617 196376 > 256⁴⁵ [i]