MinT - Best Known (50−24, 50, s)-Nets in Base 7

Best Known (50−24, 50, s)-Nets in Base 7

(50−24, 50, 102)-Net over F₇ — Constructive and digital

Digital (26, 50, 102)-net over F₇, using

trace code for nets [i] based on digital (1, 25, 51)-net over F₄₉, using
- net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(50−24, 50, 128)-Net over F₇ — Digital

Digital (26, 50, 128)-net over F₇, using

trace code for nets [i] based on digital (1, 25, 64)-net over F₄₉, using
- net from sequence [i] based on digital (1, 63)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(50−24, 50, 2919)-Net in Base 7 — Upper bound on s

There is no (26, 50, 2920)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 800650 683102 019844 273867 655150 683593 043649 > 7⁵⁰ [i]