MinT - Best Known (96−38, 96, s)-Nets in Base 9

Best Known (96−38, 96, s)-Nets in Base 9

(96−38, 96, 344)-Net over F₉ — Constructive and digital

Digital (58, 96, 344)-net over F₉, using

6 times m-reduction [i] based on digital (58, 102, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 51, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(96−38, 96, 566)-Net over F₉ — Digital

Digital (58, 96, 566)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−38, 96, 65688)-Net in Base 9 — Upper bound on s

There is no (58, 96, 65689)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 495258 595923 890593 529026 767458 396920 262014 491213 581747 499843 396715 267128 570128 057484 319385 > 9⁹⁶ [i]