MinT - Best Known (89, 89+59, s)-Nets in Base 9

Best Known (89, 89+59, s)-Nets in Base 9

(89, 89+59, 448)-Net over F₉ — Constructive and digital

Digital (89, 148, 448)-net over F₉, using

t-expansion [i] based on digital (88, 148, 448)-net over F₉, using
- 2 times m-reduction [i] based on digital (88, 150, 448)-net over F₉, using
  - trace code for nets [i] based on digital (13, 75, 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]

(89, 89+59, 768)-Net over F₉ — Digital

Digital (89, 148, 768)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+59, 100225)-Net in Base 9 — Upper bound on s

There is no (89, 148, 100226)-net in base 9, because

1 times m-reduction [i] would yield (89, 147, 100226)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 187 809181 286570 470902 011963 376916 167410 581475 149561 719264 098685 130021 548047 465386 858917 433518 610349 666514 983532 472908 531434 454685 678917 680721 > 9¹⁴⁷ [i]