MinT - Best Known (46, 46+37, s)-Nets in Base 9

Best Known (46, 46+37, s)-Nets in Base 9

(46, 46+37, 300)-Net over F₉ — Constructive and digital

Digital (46, 83, 300)-net over F₉, using

1 times m-reduction [i] based on digital (46, 84, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 42, 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]

(46, 46+37, 308)-Net over F₉ — Digital

Digital (46, 83, 308)-net over F₉, using

1 times m-reduction [i] based on digital (46, 84, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 42, 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]

(46, 46+37, 20985)-Net in Base 9 — Upper bound on s

There is no (46, 83, 20986)-net in base 9, because

1 times m-reduction [i] would yield (46, 82, 20986)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 770172 203254 207685 008375 562928 927520 477824 724798 720315 517515 575280 061750 368865 > 9⁸² [i]