MinT - Best Known (54, 107, s)-Nets in Base 16

Best Known (54, 107, s)-Nets in Base 16

(54, 107, 514)-Net over F₁₆ — Constructive and digital

Digital (54, 107, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (54, 108, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 54, 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]

(54, 107, 57042)-Net in Base 16 — Upper bound on s

There is no (54, 107, 57043)-net in base 16, because

1 times m-reduction [i] would yield (54, 106, 57043)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 334318 378509 397281 807571 913414 584510 938621 957316 986963 959649 281909 257570 883289 785146 723942 967872 743377 367559 935782 570084 719896 > 16¹⁰⁶ [i]