MinT - Best Known (58, 58+46, s)-Nets in Base 9

Best Known (58, 58+46, s)-Nets in Base 9

(58, 58+46, 320)-Net over F₉ — Constructive and digital

Digital (58, 104, 320)-net over F₉, using

2 times m-reduction [i] based on digital (58, 106, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 53, 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]

(58, 58+46, 380)-Net over F₉ — Digital

Digital (58, 104, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 52, 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]

(58, 58+46, 24319)-Net in Base 9 — Upper bound on s

There is no (58, 104, 24320)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1743 546666 437826 101333 699429 025304 546170 558501 160385 749360 309101 818525 577495 368818 685077 351881 156609 > 9¹⁰⁴ [i]