MinT - Best Known (52−24, 52, s)-Nets in Base 9

Best Known (52−24, 52, s)-Nets in Base 9

(52−24, 52, 232)-Net over F₉ — Constructive and digital

Digital (28, 52, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 26, 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]

(52−24, 52, 236)-Net over F₉ — Digital

Digital (28, 52, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 26, 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]

(52−24, 52, 9015)-Net in Base 9 — Upper bound on s

There is no (28, 52, 9016)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 778552 891098 995849 908887 999845 327769 797680 378625 > 9⁵² [i]