MinT - Best Known (86, 86+61, s)-Nets in Base 9

Best Known (86, 86+61, s)-Nets in Base 9

(86, 86+61, 344)-Net over F₉ — Constructive and digital

Digital (86, 147, 344)-net over F₉, using

t-expansion [i] based on digital (82, 147, 344)-net over F₉, using
- 3 times m-reduction [i] based on digital (82, 150, 344)-net over F₉, using
  - trace code for nets [i] based on digital (7, 75, 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]

(86, 86+61, 626)-Net over F₉ — Digital

Digital (86, 147, 626)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+61, 66307)-Net in Base 9 — Upper bound on s

There is no (86, 147, 66308)-net in base 9, because

1 times m-reduction [i] would yield (86, 146, 66308)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 873849 561000 577523 605797 364250 129255 319641 798951 858780 180347 431516 474842 466738 516554 040987 454133 812603 874439 370412 737186 274800 259832 349505 > 9¹⁴⁶ [i]