MinT - Best Known (135−54, 135, s)-Nets in Base 3

Best Known (135−54, 135, s)-Nets in Base 3

(135−54, 135, 128)-Net over F₃ — Constructive and digital

Digital (81, 135, 128)-net over F₃, using

1 times m-reduction [i] based on digital (81, 136, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 68, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(135−54, 135, 134)-Net over F₃ — Digital

Digital (81, 135, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−54, 135, 1301)-Net in Base 3 — Upper bound on s

There is no (81, 135, 1302)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26282 077333 276874 065821 588790 866211 328900 307135 558865 340535 938097 > 3¹³⁵ [i]