MinT - Best Known (95−41, 95, s)-Nets in Base 9

Best Known (95−41, 95, s)-Nets in Base 9

(95−41, 95, 320)-Net over F₉ — Constructive and digital

Digital (54, 95, 320)-net over F₉, using

3 times m-reduction [i] based on digital (54, 98, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 49, 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]

(95−41, 95, 380)-Net over F₉ — Digital

Digital (54, 95, 380)-net over F₉, using

1 times m-reduction [i] based on digital (54, 96, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 48, 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]

(95−41, 95, 31695)-Net in Base 9 — Upper bound on s

There is no (54, 95, 31696)-net in base 9, because

1 times m-reduction [i] would yield (54, 94, 31696)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 500094 109347 586072 650775 322319 250567 010533 950201 227419 323893 270006 218888 560145 572852 231681 > 9⁹⁴ [i]