MinT - Best Known (54, 54+43, s)-Nets in Base 9

Best Known (54, 54+43, s)-Nets in Base 9

(54, 54+43, 320)-Net over F₉ — Constructive and digital

Digital (54, 97, 320)-net over F₉, using

1 times m-reduction [i] based on digital (54, 98, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 49, 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]

(54, 54+43, 334)-Net over F₉ — Digital

Digital (54, 97, 334)-net over F₉, using

1 times m-reduction [i] based on digital (54, 98, 334)-net over F₉, using
- trace code for nets [i] based on digital (5, 49, 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]

(54, 54+43, 24970)-Net in Base 9 — Upper bound on s

There is no (54, 97, 24971)-net in base 9, because

1 times m-reduction [i] would yield (54, 96, 24971)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 486442 760488 163155 501352 244721 159437 851589 254838 490505 757106 420681 912611 287785 382483 326009 > 9⁹⁶ [i]