MinT - Best Known (74, 74+47, s)-Nets in Base 9

Best Known (74, 74+47, s)-Nets in Base 9

(74, 74+47, 448)-Net over F₉ — Constructive and digital

Digital (74, 121, 448)-net over F₉, using

1 times m-reduction [i] based on digital (74, 122, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 61, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(74, 74+47, 748)-Net over F₉ — Digital

Digital (74, 121, 748)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+47, 112193)-Net in Base 9 — Upper bound on s

There is no (74, 121, 112194)-net in base 9, because

1 times m-reduction [i] would yield (74, 120, 112194)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 229326 786132 408627 822389 904383 160847 267560 466646 511477 517110 931171 748100 402056 629402 076286 822955 945803 232629 296433 > 9¹²⁰ [i]