MinT - Best Known (89−39, 89, s)-Nets in Base 9

Best Known (89−39, 89, s)-Nets in Base 9

(89−39, 89, 320)-Net over F₉ — Constructive and digital

Digital (50, 89, 320)-net over F₉, using

1 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]

(89−39, 89, 334)-Net over F₉ — Digital

Digital (50, 89, 334)-net over F₉, using

1 times m-reduction [i] based on digital (50, 90, 334)-net over F₉, using
- trace code for nets [i] based on digital (5, 45, 167)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
      - a curve from the manYPoints database [i]

(89−39, 89, 26036)-Net in Base 9 — Upper bound on s

There is no (50, 89, 26037)-net in base 9, because

1 times m-reduction [i] would yield (50, 88, 26037)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 940690 441366 958905 663727 826733 812391 334478 484081 202604 491063 031513 978701 092153 569465 > 9⁸⁸ [i]