MinT - Best Known (109−46, 109, s)-Nets in Base 9

Best Known (109−46, 109, s)-Nets in Base 9

(109−46, 109, 344)-Net over F₉ — Constructive and digital

Digital (63, 109, 344)-net over F₉, using

3 times m-reduction [i] based on digital (63, 112, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 56, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(109−46, 109, 452)-Net over F₉ — Digital

Digital (63, 109, 452)-net over F₉, using

1 times m-reduction [i] based on digital (63, 110, 452)-net over F₉, using
- trace code for nets [i] based on digital (8, 55, 226)-net over F₈₁, using
  - net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
      - a curve from the manYPoints database [i]

(109−46, 109, 39218)-Net in Base 9 — Upper bound on s

There is no (63, 109, 39219)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 102 926686 929845 177656 457773 673265 466718 678754 447566 996707 166001 901862 337777 006716 502992 843050 044284 933673 > 9¹⁰⁹ [i]