MinT - Best Known (120−54, 120, s)-Nets in Base 9

Best Known (120−54, 120, s)-Nets in Base 9

(120−54, 120, 320)-Net over F₉ — Constructive and digital

Digital (66, 120, 320)-net over F₉, using

2 times m-reduction [i] based on digital (66, 122, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 61, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(120−54, 120, 380)-Net over F₉ — Digital

Digital (66, 120, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 60, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(120−54, 120, 23773)-Net in Base 9 — Upper bound on s

There is no (66, 120, 23774)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 230576 101722 085775 280820 696924 890477 373575 372260 464374 116899 871590 544234 436012 380167 553350 696407 116694 325062 190865 > 9¹²⁰ [i]