MinT - Best Known (71−33, 71, s)-Nets in Base 9

Best Known (71−33, 71, s)-Nets in Base 9

(71−33, 71, 232)-Net over F₉ — Constructive and digital

Digital (38, 71, 232)-net over F₉, using

1 times m-reduction [i] based on digital (38, 72, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 36, 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]

(71−33, 71, 236)-Net over F₉ — Digital

Digital (38, 71, 236)-net over F₉, using

1 times m-reduction [i] based on digital (38, 72, 236)-net over F₉, using
- trace code for nets [i] based on digital (2, 36, 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]

(71−33, 71, 12703)-Net in Base 9 — Upper bound on s

There is no (38, 71, 12704)-net in base 9, because

1 times m-reduction [i] would yield (38, 70, 12704)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 267019 618516 675446 001959 008159 960180 979856 099884 448900 954578 169857 > 9⁷⁰ [i]