MinT - Best Known (63, 63+27, s)-Nets in Base 9

Best Known (63, 63+27, s)-Nets in Base 9

(63, 63+27, 740)-Net over F₉ — Constructive and digital

Digital (63, 90, 740)-net over F₉, using

4 times m-reduction [i] based on digital (63, 94, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 47, 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]

(63, 63+27, 2664)-Net over F₉ — Digital

Digital (63, 90, 2664)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+27, 2416605)-Net in Base 9 — Upper bound on s

There is no (63, 90, 2416606)-net in base 9, because

1 times m-reduction [i] would yield (63, 89, 2416606)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 464150 385091 254924 800656 403008 928674 428686 390431 755831 759865 365512 163180 346405 727665 > 9⁸⁹ [i]