MinT - Best Known (53−26, 53, s)-Nets in Base 16

Best Known (53−26, 53, s)-Nets in Base 16

(53−26, 53, 514)-Net over F₁₆ — Constructive and digital

Digital (27, 53, 514)-net over F₁₆, using

1 times m-reduction [i] based on 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]

(53−26, 53, 30642)-Net in Base 16 — Upper bound on s

There is no (27, 53, 30643)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6583 815326 193827 199855 880370 684400 477842 456290 387577 864647 498936 > 16⁵³ [i]