MinT - Best Known (62, 62+53, s)-Nets in Base 9

Best Known (62, 62+53, s)-Nets in Base 9

(62, 62+53, 300)-Net over F₉ — Constructive and digital

Digital (62, 115, 300)-net over F₉, using

1 times m-reduction [i] based on digital (62, 116, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 58, 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]

(62, 62+53, 314)-Net over F₉ — Digital

Digital (62, 115, 314)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+53, 20130)-Net in Base 9 — Upper bound on s

There is no (62, 115, 20131)-net in base 9, because

1 times m-reduction [i] would yield (62, 114, 20131)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 082029 360757 296005 412166 667804 018879 095372 270086 363060 873680 348902 707310 272654 773102 973587 430848 185421 531121 > 9¹¹⁴ [i]