MinT - Best Known (87−40, 87, s)-Nets in Base 9

Best Known (87−40, 87, s)-Nets in Base 9

(87−40, 87, 232)-Net over F₉ — Constructive and digital

Digital (47, 87, 232)-net over F₉, using

3 times m-reduction [i] based on digital (47, 90, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 45, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(87−40, 87, 272)-Net over F₉ — Digital

Digital (47, 87, 272)-net over F₉, using

1 times m-reduction [i] based on digital (47, 88, 272)-net over F₉, using
- trace code for nets [i] based on digital (3, 44, 136)-net over F₈₁, using
  - net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

(87−40, 87, 14683)-Net in Base 9 — Upper bound on s

There is no (47, 87, 14684)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104630 005050 457214 928171 801652 399677 758108 072586 446009 613083 962976 651587 283443 453569 > 9⁸⁷ [i]