MinT - Best Known (52, 52+41, s)-Nets in Base 9

Best Known (52, 52+41, s)-Nets in Base 9

(52, 52+41, 320)-Net over F₉ — Constructive and digital

Digital (52, 93, 320)-net over F₉, using

1 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+41, 334)-Net over F₉ — Digital

Digital (52, 93, 334)-net over F₉, using

1 times m-reduction [i] based on digital (52, 94, 334)-net over F₉, using
- trace code for nets [i] based on digital (5, 47, 167)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
      - a curve from the manYPoints database [i]

(52, 52+41, 25440)-Net in Base 9 — Upper bound on s

There is no (52, 93, 25441)-net in base 9, because

1 times m-reduction [i] would yield (52, 92, 25441)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6172 400418 503654 448148 724702 795762 752129 775751 386250 601232 163913 721813 465801 037473 872929 > 9⁹² [i]