MinT - Best Known (50, 50+43, s)-Nets in Base 16

Best Known (50, 50+43, s)-Nets in Base 16

(50, 50+43, 520)-Net over F₁₆ — Constructive and digital

Digital (50, 93, 520)-net over F₁₆, using

1 times m-reduction [i] based on digital (50, 94, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 47, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(50, 50+43, 642)-Net over F₁₆ — Digital

Digital (50, 93, 642)-net over F₁₆, using

3 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+43, 109030)-Net in Base 16 — Upper bound on s

There is no (50, 93, 109031)-net in base 16, because

1 times m-reduction [i] would yield (50, 92, 109031)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 601 278864 019512 341123 009920 731013 496822 026198 244680 856740 245474 624077 117348 563267 153815 750723 008311 653326 794516 > 16⁹² [i]