MinT - Best Known (18−12, 18, s)-Nets in Base 256

Best Known (18−12, 18, s)-Nets in Base 256

(18−12, 18, 514)-Net over F₂₅₆ — Constructive and digital

Digital (6, 18, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 6, 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, 12, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(18−12, 18, 196968)-Net in Base 256 — Upper bound on s

There is no (6, 18, 196969)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 22 301252 279331 388463 005015 580481 155913 093196 > 256¹⁸ [i]