MinT - Best Known (85−27, 85, s)-Nets in Base 9

Best Known (85−27, 85, s)-Nets in Base 9

(85−27, 85, 448)-Net over F₉ — Constructive and digital

Digital (58, 85, 448)-net over F₉, using

5 times m-reduction [i] based on digital (58, 90, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 45, 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]

(85−27, 85, 1750)-Net over F₉ — Digital

Digital (58, 85, 1750)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−27, 85, 1037976)-Net in Base 9 — Upper bound on s

There is no (58, 85, 1037977)-net in base 9, because

1 times m-reduction [i] would yield (58, 84, 1037977)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 143 341347 455418 169707 771758 036322 966845 667024 613198 526068 893570 646433 352117 365673 > 9⁸⁴ [i]