MinT - Best Known (37, 37+24, s)-Nets in Base 9

Best Known (37, 37+24, s)-Nets in Base 9

(37, 37+24, 320)-Net over F₉ — Constructive and digital

Digital (37, 61, 320)-net over F₉, using

3 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, 37+24, 412)-Net over F₉ — Digital

Digital (37, 61, 412)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 37+24, 46874)-Net in Base 9 — Upper bound on s

There is no (37, 61, 46875)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 16173 961691 053234 957565 097597 425848 975259 028558 023947 700001 > 9⁶¹ [i]