MinT - Best Known (50−24, 50, s)-Nets in Base 16

Best Known (50−24, 50, s)-Nets in Base 16

(50−24, 50, 516)-Net over F₁₆ — Constructive and digital

Digital (26, 50, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 25, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(50−24, 50, 578)-Net over F₁₆ — Digital

Digital (26, 50, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 25, 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]

(50−24, 50, 36674)-Net in Base 16 — Upper bound on s

There is no (26, 50, 36675)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 607291 801401 610001 354934 918525 237848 571057 602953 756903 163376 > 16⁵⁰ [i]