MinT - Best Known (48, 70, s)-Nets in Base 9

Best Known (48, 70, s)-Nets in Base 9

(48, 70, 448)-Net over F₉ — Constructive and digital

Digital (48, 70, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 35, 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]

(48, 70, 1656)-Net over F₉ — Digital

Digital (48, 70, 1656)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 70, 725057)-Net in Base 9 — Upper bound on s

There is no (48, 70, 725058)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 265797 831918 707176 653361 594584 916607 982507 421358 113449 097349 570545 > 9⁷⁰ [i]