MinT - Best Known (39−19, 39, s)-Nets in Base 16

Best Known (39−19, 39, s)-Nets in Base 16

(39−19, 39, 514)-Net over F₁₆ — Constructive and digital

Digital (20, 39, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (20, 40, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 20, 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]

(39−19, 39, 33547)-Net in Base 16 — Upper bound on s

There is no (20, 39, 33548)-net in base 16, because

1 times m-reduction [i] would yield (20, 38, 33548)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 5709 444988 527757 286513 329295 313080 811694 567081 > 16³⁸ [i]