MinT - Best Known (10, 10+20, s)-Nets in Base 256

Best Known (10, 10+20, s)-Nets in Base 256

(10, 10+20, 514)-Net over F₂₅₆ — Constructive and digital

Digital (10, 30, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 10, 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, 20, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(10, 10+20, 297954)-Net in Base 256 — Upper bound on s

There is no (10, 30, 297955)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 1 766898 943510 584698 903473 145774 987298 608781 244488 513601 468777 006293 445876 > 256³⁰ [i]