MinT - Best Known (99−45, 99, s)-Nets in Base 9

Best Known (99−45, 99, s)-Nets in Base 9

(99−45, 99, 300)-Net over F₉ — Constructive and digital

Digital (54, 99, 300)-net over F₉, using

1 times m-reduction [i] based on digital (54, 100, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 50, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(99−45, 99, 308)-Net over F₉ — Digital

Digital (54, 99, 308)-net over F₉, using

1 times m-reduction [i] based on digital (54, 100, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 50, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(99−45, 99, 20146)-Net in Base 9 — Upper bound on s

There is no (54, 99, 20147)-net in base 9, because

1 times m-reduction [i] would yield (54, 98, 20147)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3281 874567 244831 923202 384276 014631 998038 089972 731554 275425 566608 479627 631901 018468 266580 192145 > 9⁹⁸ [i]