MinT - Best Known (81−36, 81, s)-Nets in Base 9

Best Known (81−36, 81, s)-Nets in Base 9

(81−36, 81, 300)-Net over F₉ — Constructive and digital

Digital (45, 81, 300)-net over F₉, using

1 times m-reduction [i] based on digital (45, 82, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 41, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(81−36, 81, 308)-Net over F₉ — Digital

Digital (45, 81, 308)-net over F₉, using

1 times m-reduction [i] based on digital (45, 82, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 41, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(81−36, 81, 18572)-Net in Base 9 — Upper bound on s

There is no (45, 81, 18573)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 196642 928794 135664 087563 785554 660369 930978 769439 171905 457596 848782 260391 589905 > 9⁸¹ [i]