MinT - Best Known (132−45, 132, s)-Nets in Base 9

Best Known (132−45, 132, s)-Nets in Base 9

(132−45, 132, 740)-Net over F₉ — Constructive and digital

Digital (87, 132, 740)-net over F₉, using

10 times m-reduction [i] based on digital (87, 142, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 71, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(132−45, 132, 1594)-Net over F₉ — Digital

Digital (87, 132, 1594)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−45, 132, 544293)-Net in Base 9 — Upper bound on s

There is no (87, 132, 544294)-net in base 9, because

1 times m-reduction [i] would yield (87, 131, 544294)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101340 662275 908773 784113 781060 411023 512320 799675 056152 282447 443186 237967 451666 065689 846230 027652 991325 395189 272963 315522 798305 > 9¹³¹ [i]