MinT - Best Known (25, 49, s)-Nets in Base 16

Best Known (25, 49, s)-Nets in Base 16

(25, 49, 514)-Net over F₁₆ — Constructive and digital

Digital (25, 49, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (25, 50, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 25, 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]

(25, 49, 29107)-Net in Base 16 — Upper bound on s

There is no (25, 49, 29108)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 100469 516474 545686 950483 376642 752104 229974 407108 300006 855916 > 16⁴⁹ [i]