MinT - Best Known (50−25, 50, s)-Nets in Base 16

Best Known (50−25, 50, s)-Nets in Base 16

(50−25, 50, 514)-Net over F₁₆ — Constructive and digital

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]

(50−25, 50, 29107)-Net in Base 16 — Upper bound on s

There is no (25, 50, 29108)-net in base 16, because

1 times m-reduction [i] would yield (25, 49, 29108)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 100469 516474 545686 950483 376642 752104 229974 407108 300006 855916 > 16⁴⁹ [i]