MinT - Best Known (86, 86+55, s)-Nets in Base 9

Best Known (86, 86+55, s)-Nets in Base 9

(86, 86+55, 448)-Net over F₉ — Constructive and digital

Digital (86, 141, 448)-net over F₉, using

5 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+55, 825)-Net over F₉ — Digital

Digital (86, 141, 825)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+55, 121110)-Net in Base 9 — Upper bound on s

There is no (86, 141, 121111)-net in base 9, because

1 times m-reduction [i] would yield (86, 140, 121111)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 263503 028743 960027 892856 250862 779439 746557 464862 197122 413402 893247 980144 988432 055793 000112 787441 433009 990815 602531 435872 104653 897321 > 9¹⁴⁰ [i]