MinT - Best Known (58−26, 58, s)-Nets in Base 9

Best Known (58−26, 58, s)-Nets in Base 9

(58−26, 58, 232)-Net over F₉ — Constructive and digital

Digital (32, 58, 232)-net over F₉, using

2 times m-reduction [i] based on digital (32, 60, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 30, 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]

(58−26, 58, 272)-Net over F₉ — Digital

Digital (32, 58, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 29, 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]

(58−26, 58, 12806)-Net in Base 9 — Upper bound on s

There is no (32, 58, 12807)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22 185316 033277 551446 772785 081670 269021 136261 867072 652505 > 9⁵⁸ [i]