MinT - Best Known (109−39, 109, s)-Nets in Base 9

Best Known (109−39, 109, s)-Nets in Base 9

(109−39, 109, 448)-Net over F₉ — Constructive and digital

Digital (70, 109, 448)-net over F₉, using

5 times m-reduction [i] based on digital (70, 114, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 57, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(109−39, 109, 1044)-Net over F₉ — Digital

Digital (70, 109, 1044)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−39, 109, 263161)-Net in Base 9 — Upper bound on s

There is no (70, 109, 263162)-net in base 9, because

1 times m-reduction [i] would yield (70, 108, 263162)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 434368 310003 570614 749059 742930 259079 362598 531144 931829 349822 333948 033029 153104 417465 973022 621340 972465 > 9¹⁰⁸ [i]