MinT - Best Known (44, 44+35, s)-Nets in Base 9

Best Known (44, 44+35, s)-Nets in Base 9

(44, 44+35, 300)-Net over F₉ — Constructive and digital

Digital (44, 79, 300)-net over F₉, using

1 times m-reduction [i] based on digital (44, 80, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 40, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(44, 44+35, 308)-Net over F₉ — Digital

Digital (44, 79, 308)-net over F₉, using

1 times m-reduction [i] based on digital (44, 80, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 40, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(44, 44+35, 21425)-Net in Base 9 — Upper bound on s

There is no (44, 79, 21426)-net in base 9, because

1 times m-reduction [i] would yield (44, 78, 21426)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 269 741357 314613 154101 400884 512073 493374 620555 074122 243778 772468 443455 704209 > 9⁷⁸ [i]