MinT - Best Known (141−43, 141, s)-Nets in Base 9

Best Known (141−43, 141, s)-Nets in Base 9

(141−43, 141, 760)-Net over F₉ — Constructive and digital

Digital (98, 141, 760)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 23, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. digital (75, 118, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 59, 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]

(141−43, 141, 3319)-Net over F₉ — Digital

Digital (98, 141, 3319)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−43, 141, 2494693)-Net in Base 9 — Upper bound on s

There is no (98, 141, 2494694)-net in base 9, because

1 times m-reduction [i] would yield (98, 140, 2494694)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 260416 524673 218420 201738 426931 042805 127234 989806 335638 353693 293727 239787 105204 391729 247000 172131 038104 892486 782425 135895 373504 560497 > 9¹⁴⁰ [i]