MinT - Best Known (140−54, 140, s)-Nets in Base 9

Best Known (140−54, 140, s)-Nets in Base 9

(140−54, 140, 740)-Net over F₉ — Constructive and digital

Digital (86, 140, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 70, 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]

(140−54, 140, 871)-Net over F₉ — Digital

Digital (86, 140, 871)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−54, 140, 121110)-Net in Base 9 — Upper bound on s

There is no (86, 140, 121111)-net in base 9, because

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]