MinT - Best Known (43, 43+31, s)-Nets in Base 9

Best Known (43, 43+31, s)-Nets in Base 9

(43, 43+31, 320)-Net over F₉ — Constructive and digital

Digital (43, 74, 320)-net over F₉, using

2 times m-reduction [i] based on digital (43, 76, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 38, 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]

(43, 43+31, 380)-Net over F₉ — Digital

Digital (43, 74, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 37, 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]

(43, 43+31, 35362)-Net in Base 9 — Upper bound on s

There is no (43, 74, 35363)-net in base 9, because

1 times m-reduction [i] would yield (43, 73, 35363)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4567 949482 015794 806905 062357 470896 208246 817582 272182 854629 373317 723625 > 9⁷³ [i]