MinT - Best Known (48, 48+23, s)-Nets in Base 9

Best Known (48, 48+23, s)-Nets in Base 9

(48, 48+23, 364)-Net over F₉ — Constructive and digital

Digital (48, 71, 364)-net over F₉, using

9¹ times duplication [i] based on digital (47, 70, 364)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 22, 164)-net over F₉, using
    - trace code for nets [i] based on digital (0, 11, 82)-net over F₈₁, using
      - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
  2. digital (25, 48, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 24, 100)-net over F₈₁, using
      - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]

(48, 48+23, 1370)-Net over F₉ — Digital

Digital (48, 71, 1370)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+23, 725057)-Net in Base 9 — Upper bound on s

There is no (48, 71, 725058)-net in base 9, because

1 times m-reduction [i] would yield (48, 70, 725058)-net in base 9, but
- 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]