MinT - Best Known (54−27, 54, s)-Nets in Base 16

Best Known (54−27, 54, s)-Nets in Base 16

(54−27, 54, 514)-Net over F₁₆ — Constructive and digital

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]

(54−27, 54, 30642)-Net in Base 16 — Upper bound on s

There is no (27, 54, 30643)-net in base 16, because

1 times m-reduction [i] would yield (27, 53, 30643)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6583 815326 193827 199855 880370 684400 477842 456290 387577 864647 498936 > 16⁵³ [i]