MinT - Best Known (146−60, 146, s)-Nets in Base 9

Best Known (146−60, 146, s)-Nets in Base 9

(146−60, 146, 448)-Net over F₉ — Constructive and digital

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]

(146−60, 146, 652)-Net over F₉ — Digital

Digital (86, 146, 652)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−60, 146, 66307)-Net in Base 9 — Upper bound on s

There is no (86, 146, 66308)-net in base 9, because

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]