MinT - Best Known (51, 51+45, s)-Nets in Base 9

Best Known (51, 51+45, s)-Nets in Base 9

(51, 51+45, 232)-Net over F₉ — Constructive and digital

Digital (51, 96, 232)-net over F₉, using

2 times m-reduction [i] based on digital (51, 98, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 49, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(51, 51+45, 272)-Net over F₉ — Digital

Digital (51, 96, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 48, 136)-net over F₈₁, using
- net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(51, 51+45, 14926)-Net in Base 9 — Upper bound on s

There is no (51, 96, 14927)-net in base 9, because

1 times m-reduction [i] would yield (51, 95, 14927)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 498667 489304 962915 259632 373409 013432 569174 623064 044369 501742 052615 672660 225718 021315 702865 > 9⁹⁵ [i]