MinT - Best Known (53, 53+41, s)-Nets in Base 9

Best Known (53, 53+41, s)-Nets in Base 9

(53, 53+41, 320)-Net over F₉ — Constructive and digital

Digital (53, 94, 320)-net over F₉, using

2 times m-reduction [i] based on digital (53, 96, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 48, 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]

(53, 53+41, 380)-Net over F₉ — Digital

Digital (53, 94, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 47, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(53, 53+41, 28396)-Net in Base 9 — Upper bound on s

There is no (53, 94, 28397)-net in base 9, because

1 times m-reduction [i] would yield (53, 93, 28397)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55564 011446 359949 754146 525422 190553 106626 869731 681611 068675 308972 258402 922974 877578 094241 > 9⁹³ [i]