MinT - Best Known (70−32, 70, s)-Nets in Base 9

Best Known (70−32, 70, s)-Nets in Base 9

(70−32, 70, 232)-Net over F₉ — Constructive and digital

Digital (38, 70, 232)-net over F₉, using

2 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]

(70−32, 70, 272)-Net over F₉ — Digital

Digital (38, 70, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 35, 136)-net over F₈₁, using
- net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(70−32, 70, 12703)-Net in Base 9 — Upper bound on s

There is no (38, 70, 12704)-net in base 9, because

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]