MinT - Best Known (98, 98+42, s)-Nets in Base 9

Best Known (98, 98+42, s)-Nets in Base 9

(98, 98+42, 768)-Net over F₉ — Constructive and digital

Digital (98, 140, 768)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 24, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. digital (74, 116, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 58, 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]

(98, 98+42, 3678)-Net over F₉ — Digital

Digital (98, 140, 3678)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+42, 2494693)-Net in Base 9 — Upper bound on s

There is no (98, 140, 2494694)-net in base 9, because

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]