MinT - Best Known (140−45, 140, s)-Nets in Base 9

Best Known (140−45, 140, s)-Nets in Base 9

(140−45, 140, 740)-Net over F₉ — Constructive and digital

Digital (95, 140, 740)-net over F₉, using

t-expansion [i] based on digital (91, 140, 740)-net over F₉, using
- 10 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 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]

(140−45, 140, 2366)-Net over F₉ — Digital

Digital (95, 140, 2366)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−45, 140, 1210140)-Net in Base 9 — Upper bound on s

There is no (95, 140, 1210141)-net in base 9, because

1 times m-reduction [i] would yield (95, 139, 1210141)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 362236 316227 208222 578326 305263 303309 313065 737899 514094 448502 439372 828089 109797 376376 357746 378287 668956 949942 114913 656385 709837 016369 > 9¹³⁹ [i]