MinT - Best Known (47, 93, s)-Nets in Base 16

Best Known (47, 93, s)-Nets in Base 16

(47, 93, 514)-Net over F₁₆ — Constructive and digital

Digital (47, 93, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (47, 94, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 47, 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]

(47, 93, 46460)-Net in Base 16 — Upper bound on s

There is no (47, 93, 46461)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9623 549324 205757 245918 414462 766386 258584 074212 784025 346725 444509 195132 769602 450356 029505 471265 168346 257597 165096 > 16⁹³ [i]