MinT - Best Known (75−34, 75, s)-Nets in Base 16

Best Known (75−34, 75, s)-Nets in Base 16

(75−34, 75, 520)-Net over F₁₆ — Constructive and digital

Digital (41, 75, 520)-net over F₁₆, using

1 times m-reduction [i] based on digital (41, 76, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 38, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(75−34, 75, 642)-Net over F₁₆ — Digital

Digital (41, 75, 642)-net over F₁₆, using

3 times m-reduction [i] based on digital (41, 78, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 39, 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]

(75−34, 75, 98199)-Net in Base 16 — Upper bound on s

There is no (41, 75, 98200)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 037346 076885 497052 635412 968846 084256 088338 529335 440676 691395 188619 613375 939486 659622 688501 > 16⁷⁵ [i]