MinT - Best Known (31, 57, s)-Nets in Base 16

Best Known (31, 57, s)-Nets in Base 16

(31, 57, 518)-Net over F₁₆ — Constructive and digital

Digital (31, 57, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (31, 58, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 29, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(31, 57, 642)-Net over F₁₆ — Digital

Digital (31, 57, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (31, 58, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 29, 321)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(31, 57, 71924)-Net in Base 16 — Upper bound on s

There is no (31, 57, 71925)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 431 403173 378226 817076 015979 458784 102217 648414 046714 662970 993614 395376 > 16⁵⁷ [i]