MinT - Best Known (13, 13+27, s)-Nets in Base 256

Best Known (13, 13+27, s)-Nets in Base 256

(13, 13+27, 514)-Net over F₂₅₆ — Constructive and digital

Digital (13, 40, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 13, 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, 27, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(13, 13+27, 372888)-Net in Base 256 — Upper bound on s

There is no (13, 40, 372889)-net in base 256, because

1 times m-reduction [i] would yield (13, 39, 372889)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 8343 880631 087922 613330 201678 486204 021964 091048 551120 225935 397146 216082 407087 391459 097953 495536 > 256³⁹ [i]