MinT - Best Known (44, 71, s)-Nets in Base 16

Best Known (44, 71, s)-Nets in Base 16

(44, 71, 559)-Net over F₁₆ — Constructive and digital

Digital (44, 71, 559)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (4, 17, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]
2. digital (27, 54, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 27, 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]

(44, 71, 1379)-Net over F₁₆ — Digital

Digital (44, 71, 1379)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 71, 1150893)-Net in Base 16 — Upper bound on s

There is no (44, 71, 1150894)-net in base 16, because

1 times m-reduction [i] would yield (44, 70, 1150894)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 942669 731788 186556 732710 203022 352048 292123 354224 052976 005959 741471 676380 955843 266331 > 16⁷⁰ [i]