MinT - Best Known (39−17, 39, s)-Nets in Base 16

Best Known (39−17, 39, s)-Nets in Base 16

(39−17, 39, 518)-Net over F₁₆ — Constructive and digital

Digital (22, 39, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (22, 40, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 20, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(39−17, 39, 642)-Net over F₁₆ — Digital

Digital (22, 39, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (22, 40, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 20, 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]

(39−17, 39, 131569)-Net in Base 16 — Upper bound on s

There is no (22, 39, 131570)-net in base 16, because

1 times m-reduction [i] would yield (22, 38, 131570)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 5709 144717 496493 697660 966285 760651 320809 432026 > 16³⁸ [i]