MinT - Best Known (99−43, 99, s)-Nets in Base 9

Best Known (99−43, 99, s)-Nets in Base 9

(99−43, 99, 320)-Net over F₉ — Constructive and digital

Digital (56, 99, 320)-net over F₉, using

3 times m-reduction [i] based on digital (56, 102, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 51, 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]

(99−43, 99, 380)-Net over F₉ — Digital

Digital (56, 99, 380)-net over F₉, using

1 times m-reduction [i] based on digital (56, 100, 380)-net over F₉, using
- trace code for nets [i] based on digital (6, 50, 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]

(99−43, 99, 30786)-Net in Base 9 — Upper bound on s

There is no (56, 99, 30787)-net in base 9, because

1 times m-reduction [i] would yield (56, 98, 30787)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3280 948094 205557 998231 438334 006634 960680 744907 166633 436262 119179 815806 148759 997731 447404 687097 > 9⁹⁸ [i]