MinT - Best Known (53−23, 53, s)-Nets in Base 9

Best Known (53−23, 53, s)-Nets in Base 9

(53−23, 53, 232)-Net over F₉ — Constructive and digital

Digital (30, 53, 232)-net over F₉, using

3 times m-reduction [i] based on digital (30, 56, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 28, 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]

(53−23, 53, 272)-Net over F₉ — Digital

Digital (30, 53, 272)-net over F₉, using

1 times m-reduction [i] based on digital (30, 54, 272)-net over F₉, using
- trace code for nets [i] based on digital (3, 27, 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]

(53−23, 53, 19895)-Net in Base 9 — Upper bound on s

There is no (30, 53, 19896)-net in base 9, because

1 times m-reduction [i] would yield (30, 52, 19896)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 762639 536403 363304 230114 970112 732001 166600 065089 > 9⁵² [i]