MinT - Best Known (40, 40+36, s)-Nets in Base 9

Best Known (40, 40+36, s)-Nets in Base 9

(40, 40+36, 232)-Net over F₉ — Constructive and digital

Digital (40, 76, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 38, 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]

(40, 40+36, 236)-Net over F₉ — Digital

Digital (40, 76, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 38, 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]

(40, 40+36, 10083)-Net in Base 9 — Upper bound on s

There is no (40, 76, 10084)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 334235 621481 142530 955737 477930 659379 372666 400772 286063 187342 628904 555201 > 9⁷⁶ [i]