MinT - Best Known (52−23, 52, s)-Nets in Base 9

Best Known (52−23, 52, s)-Nets in Base 9

(52−23, 52, 232)-Net over F₉ — Constructive and digital

Digital (29, 52, 232)-net over F₉, using

2 times m-reduction [i] based on digital (29, 54, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 27, 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]

(52−23, 52, 272)-Net over F₉ — Digital

Digital (29, 52, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 26, 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]

(52−23, 52, 16291)-Net in Base 9 — Upper bound on s

There is no (29, 52, 16292)-net in base 9, because

1 times m-reduction [i] would yield (29, 51, 16292)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 638966 924859 127211 870356 967463 083270 736682 753505 > 9⁵¹ [i]