MinT - Best Known (43−29, 43, s)-Nets in Base 256

Best Known (43−29, 43, s)-Nets in Base 256

(43−29, 43, 514)-Net over F₂₅₆ — Constructive and digital

Digital (14, 43, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 14, 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, 29, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(43−29, 43, 397768)-Net in Base 256 — Upper bound on s

There is no (14, 43, 397769)-net in base 256, because

1 times m-reduction [i] would yield (14, 42, 397769)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 139986 913238 851807 660221 747758 252073 192022 582768 955489 423013 350779 949346 784018 081190 900896 203499 879456 > 256⁴² [i]