MinT - Best Known (4, 4+9, s)-Nets in Base 256

Best Known (4, 4+9, s)-Nets in Base 256

(4, 4+9, 514)-Net over F₂₅₆ — Constructive and digital

Digital (4, 13, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 4, 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, 9, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(4, 4+9, 145622)-Net in Base 256 — Upper bound on s

There is no (4, 13, 145623)-net in base 256, because

1 times m-reduction [i] would yield (4, 12, 145623)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 79229 598661 084223 079440 300611 > 256¹² [i]