MinT - Best Known (67, 67+58, s)-Nets in Base 9

Best Known (67, 67+58, s)-Nets in Base 9

(67, 67+58, 300)-Net over F₉ — Constructive and digital

Digital (67, 125, 300)-net over F₉, using

1 times m-reduction [i] based on digital (67, 126, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 63, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(67, 67+58, 327)-Net over F₉ — Digital

Digital (67, 125, 327)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+58, 18912)-Net in Base 9 — Upper bound on s

There is no (67, 125, 18913)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 190919 896981 548951 927345 417063 294046 789131 225480 564960 000311 462983 386699 607498 010569 313576 102901 617664 636913 052083 752297 > 9¹²⁵ [i]