MinT - Best Known (134, 134+51, s)-Nets in Base 3

Best Known (134, 134+51, s)-Nets in Base 3

(134, 134+51, 282)-Net over F₃ — Constructive and digital

Digital (134, 185, 282)-net over F₃, using

1 times m-reduction [i] based on digital (134, 186, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 62, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(134, 134+51, 552)-Net over F₃ — Digital

Digital (134, 185, 552)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+51, 16503)-Net in Base 3 — Upper bound on s

There is no (134, 185, 16504)-net in base 3, because

1 times m-reduction [i] would yield (134, 184, 16504)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6179 172205 856713 577838 893892 992896 389038 550271 618879 016054 403426 627087 471053 157136 422513 > 3¹⁸⁴ [i]