MinT - Best Known (134−61, 134, s)-Nets in Base 9

Best Known (134−61, 134, s)-Nets in Base 9

(134−61, 134, 320)-Net over F₉ — Constructive and digital

Digital (73, 134, 320)-net over F₉, using

2 times m-reduction [i] based on digital (73, 136, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 68, 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]

(134−61, 134, 380)-Net over F₉ — Digital

Digital (73, 134, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 67, 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]

(134−61, 134, 25577)-Net in Base 9 — Upper bound on s

There is no (73, 134, 25578)-net in base 9, because

1 times m-reduction [i] would yield (73, 133, 25578)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 209711 068527 622932 192940 139367 975984 228558 998030 400360 252546 841804 724014 086401 844443 354965 383818 742891 275385 532277 646040 882337 > 9¹³³ [i]