MinT - Best Known (62, 111, s)-Nets in Base 9

Best Known (62, 111, s)-Nets in Base 9

(62, 111, 320)-Net over F₉ — Constructive and digital

Digital (62, 111, 320)-net over F₉, using

3 times m-reduction [i] based on digital (62, 114, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 57, 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]

(62, 111, 380)-Net over F₉ — Digital

Digital (62, 111, 380)-net over F₉, using

1 times m-reduction [i] based on digital (62, 112, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 56, 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]

(62, 111, 28951)-Net in Base 9 — Upper bound on s

There is no (62, 111, 28952)-net in base 9, because

1 times m-reduction [i] would yield (62, 110, 28952)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 926 739742 379037 310698 998496 915964 070486 105721 571042 507081 025908 616906 721780 234394 865445 725614 276679 986689 > 9¹¹⁰ [i]