MinT - Best Known (90−26, 90, s)-Nets in Base 9

Best Known (90−26, 90, s)-Nets in Base 9

(90−26, 90, 740)-Net over F₉ — Constructive and digital

Digital (64, 90, 740)-net over F₉, using

6 times m-reduction [i] based on digital (64, 96, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 48, 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]

(90−26, 90, 3478)-Net over F₉ — Digital

Digital (64, 90, 3478)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−26, 90, 2861602)-Net in Base 9 — Upper bound on s

There is no (64, 90, 2861603)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 177467 403528 602356 472671 844135 263825 912041 689846 893789 320541 700690 339452 253852 795705 > 9⁹⁰ [i]