MinT - Best Known (59−29, 59, s)-Nets in Base 16

Best Known (59−29, 59, s)-Nets in Base 16

(59−29, 59, 514)-Net over F₁₆ — Constructive and digital

Digital (30, 59, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (30, 60, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 30, 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]

(59−29, 59, 39244)-Net in Base 16 — Upper bound on s

There is no (30, 59, 39245)-net in base 16, because

1 times m-reduction [i] would yield (30, 58, 39245)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6902 420326 678168 408174 939021 218605 734555 236090 221206 174718 284909 420576 > 16⁵⁸ [i]