MinT - Best Known (39, 39+27, s)-Nets in Base 9

Best Known (39, 39+27, s)-Nets in Base 9

(39, 39+27, 320)-Net over F₉ — Constructive and digital

Digital (39, 66, 320)-net over F₉, using

2 times m-reduction [i] based on digital (39, 68, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 34, 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]

(39, 39+27, 380)-Net over F₉ — Digital

Digital (39, 66, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 33, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(39, 39+27, 41826)-Net in Base 9 — Upper bound on s

There is no (39, 66, 41827)-net in base 9, because

1 times m-reduction [i] would yield (39, 65, 41827)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 106 134334 605080 606979 471181 341824 415261 461235 392992 436531 041593 > 9⁶⁵ [i]