MinT - Best Known (52, 52+43, s)-Nets in Base 9

Best Known (52, 52+43, s)-Nets in Base 9

(52, 52+43, 300)-Net over F₉ — Constructive and digital

Digital (52, 95, 300)-net over F₉, using

1 times m-reduction [i] based on digital (52, 96, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 48, 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]

(52, 52+43, 308)-Net over F₉ — Digital

Digital (52, 95, 308)-net over F₉, using

1 times m-reduction [i] based on digital (52, 96, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 48, 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]

(52, 52+43, 20253)-Net in Base 9 — Upper bound on s

There is no (52, 95, 20254)-net in base 9, because

1 times m-reduction [i] would yield (52, 94, 20254)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 499982 516255 749308 401788 801336 205616 252448 471643 320137 128834 630675 695652 209632 746512 123953 > 9⁹⁴ [i]