MinT - Best Known (75−37, 75, s)-Nets in Base 16

Best Known (75−37, 75, s)-Nets in Base 16

(75−37, 75, 514)-Net over F₁₆ — Constructive and digital

Digital (38, 75, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (38, 76, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 38, 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]

(75−37, 75, 44896)-Net in Base 16 — Upper bound on s

There is no (38, 75, 44897)-net in base 16, because

1 times m-reduction [i] would yield (38, 74, 44897)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 127321 603894 296909 532739 127028 160250 659430 207866 496294 097237 962047 861808 800393 320126 615216 > 16⁷⁴ [i]