MinT - Best Known (55, 94, s)-Nets in Base 9

Best Known (55, 94, s)-Nets in Base 9

(55, 94, 344)-Net over F₉ — Constructive and digital

Digital (55, 94, 344)-net over F₉, using

2 times m-reduction [i] based on digital (55, 96, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 48, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(55, 94, 452)-Net over F₉ — Digital

Digital (55, 94, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 47, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(55, 94, 46428)-Net in Base 9 — Upper bound on s

There is no (55, 94, 46429)-net in base 9, because

1 times m-reduction [i] would yield (55, 93, 46429)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55543 548673 649035 809769 336428 711057 557253 922447 372513 733368 681261 407336 394117 615735 343481 > 9⁹³ [i]