MinT - Best Known (50, 50+41, s)-Nets in Base 16

Best Known (50, 50+41, s)-Nets in Base 16

(50, 50+41, 522)-Net over F₁₆ — Constructive and digital

Digital (50, 91, 522)-net over F₁₆, using

1 times m-reduction [i] based on digital (50, 92, 522)-net over F₁₆, using
- trace code for nets [i] based on digital (4, 46, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(50, 50+41, 642)-Net over F₁₆ — Digital

Digital (50, 91, 642)-net over F₁₆, using

5 times m-reduction [i] based on digital (50, 96, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 48, 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]

(50, 50+41, 145118)-Net in Base 16 — Upper bound on s

There is no (50, 91, 145119)-net in base 16, because

1 times m-reduction [i] would yield (50, 90, 145119)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 348737 502180 283454 284443 908266 865271 073623 097622 704194 489083 993181 681795 063468 996381 823942 594166 743095 814451 > 16⁹⁰ [i]