MinT - Best Known (75−36, 75, s)-Nets in Base 16

Best Known (75−36, 75, s)-Nets in Base 16

(75−36, 75, 516)-Net over F₁₆ — Constructive and digital

Digital (39, 75, 516)-net over F₁₆, using

1 times m-reduction [i] based on digital (39, 76, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 38, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(75−36, 75, 578)-Net over F₁₆ — Digital

Digital (39, 75, 578)-net over F₁₆, using

1 times m-reduction [i] based on digital (39, 76, 578)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 38, 289)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(75−36, 75, 52375)-Net in Base 16 — Upper bound on s

There is no (39, 75, 52376)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 037657 093246 864662 043044 190809 777447 122752 599075 823551 750451 713336 366868 702580 228744 189321 > 16⁷⁵ [i]