MinT - Best Known (80−38, 80, s)-Nets in Base 9

Best Known (80−38, 80, s)-Nets in Base 9

(80−38, 80, 232)-Net over F₉ — Constructive and digital

Digital (42, 80, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 40, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(80−38, 80, 236)-Net over F₉ — Digital

Digital (42, 80, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 40, 118)-net over F₈₁, using
- net from sequence [i] based on digital (2, 117)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 118, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(80−38, 80, 10315)-Net in Base 9 — Upper bound on s

There is no (42, 80, 10316)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21848 473869 527325 768058 298848 269457 665815 505241 592268 042237 418365 790084 785057 > 9⁸⁰ [i]