MinT - Best Known (67, 67+37, s)-Nets in Base 9

Best Known (67, 67+37, s)-Nets in Base 9

(67, 67+37, 448)-Net over F₉ — Constructive and digital

Digital (67, 104, 448)-net over F₉, using

4 times m-reduction [i] based on digital (67, 108, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 54, 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]

(67, 67+37, 1037)-Net over F₉ — Digital

Digital (67, 104, 1037)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+37, 272527)-Net in Base 9 — Upper bound on s

There is no (67, 104, 272528)-net in base 9, because

1 times m-reduction [i] would yield (67, 103, 272528)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 193 636585 734609 020484 689768 015092 703086 164416 641728 905960 268952 541159 607348 243522 551013 273507 640065 > 9¹⁰³ [i]