MinT - Best Known (37, 62, s)-Nets in Base 9

Best Known (37, 62, s)-Nets in Base 9

(37, 62, 320)-Net over F₉ — Constructive and digital

Digital (37, 62, 320)-net over F₉, using

2 times m-reduction [i] based on digital (37, 64, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 32, 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]

(37, 62, 380)-Net over F₉ — Digital

Digital (37, 62, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 31, 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]

(37, 62, 46874)-Net in Base 9 — Upper bound on s

There is no (37, 62, 46875)-net in base 9, because

1 times m-reduction [i] would yield (37, 61, 46875)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 16173 961691 053234 957565 097597 425848 975259 028558 023947 700001 > 9⁶¹ [i]