MinT - Best Known (50, 87, s)-Nets in Base 9

Best Known (50, 87, s)-Nets in Base 9

(50, 87, 320)-Net over F₉ — Constructive and digital

Digital (50, 87, 320)-net over F₉, using

3 times m-reduction [i] based on digital (50, 90, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 45, 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]

(50, 87, 380)-Net over F₉ — Digital

Digital (50, 87, 380)-net over F₉, using

1 times m-reduction [i] based on digital (50, 88, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 44, 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]

(50, 87, 34202)-Net in Base 9 — Upper bound on s

There is no (50, 87, 34203)-net in base 9, because

1 times m-reduction [i] would yield (50, 86, 34203)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11611 563727 094916 046134 704300 115356 392707 299230 937814 187271 508470 986099 233750 086065 > 9⁸⁶ [i]