MinT - Best Known (49−33, 49, s)-Nets in Base 256

Best Known (49−33, 49, s)-Nets in Base 256

(49−33, 49, 514)-Net over F₂₅₆ — Constructive and digital

Digital (16, 49, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 16, 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, 33, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(49−33, 49, 447415)-Net in Base 256 — Upper bound on s

There is no (16, 49, 447416)-net in base 256, because

1 times m-reduction [i] would yield (16, 48, 447416)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 39 402603 619526 973260 727868 775842 705842 453574 386243 997643 765833 637866 406034 396335 646626 518942 715058 817862 163162 916531 > 256⁴⁸ [i]