MinT - Best Known (86, 86+57, s)-Nets in Base 9

Best Known (86, 86+57, s)-Nets in Base 9

(86, 86+57, 448)-Net over F₉ — Constructive and digital

Digital (86, 143, 448)-net over F₉, using

3 times m-reduction [i] based on digital (86, 146, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 73, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(86, 86+57, 747)-Net over F₉ — Digital

Digital (86, 143, 747)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+57, 97546)-Net in Base 9 — Upper bound on s

There is no (86, 143, 97547)-net in base 9, because

1 times m-reduction [i] would yield (86, 142, 97547)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3180 441668 222470 777005 783532 938899 315095 818926 143878 434526 499317 931471 331949 223957 417863 265223 745556 576524 208399 207021 093780 032108 398241 > 9¹⁴² [i]