MinT - Best Known (52, 52+39, s)-Nets in Base 9

Best Known (52, 52+39, s)-Nets in Base 9

(52, 52+39, 320)-Net over F₉ — Constructive and digital

Digital (52, 91, 320)-net over F₉, using

3 times m-reduction [i] based on digital (52, 94, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 47, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(52, 52+39, 380)-Net over F₉ — Digital

Digital (52, 91, 380)-net over F₉, using

1 times m-reduction [i] based on digital (52, 92, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 46, 190)-net over F₈₁, using
  - net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
      - a curve from the manYPoints database [i]

(52, 52+39, 32814)-Net in Base 9 — Upper bound on s

There is no (52, 91, 32815)-net in base 9, because

1 times m-reduction [i] would yield (52, 90, 32815)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 181660 638136 728694 101724 095441 082671 341435 907719 239520 800555 431545 732688 514522 474985 > 9⁹⁰ [i]