MinT - Best Known (134−36, 134, s)-Nets in Base 3

Best Known (134−36, 134, s)-Nets in Base 3

(134−36, 134, 252)-Net over F₃ — Constructive and digital

Digital (98, 134, 252)-net over F₃, using

1 times m-reduction [i] based on digital (98, 135, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 45, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(134−36, 134, 469)-Net over F₃ — Digital

Digital (98, 134, 469)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−36, 134, 13441)-Net in Base 3 — Upper bound on s

There is no (98, 134, 13442)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8604 270509 443854 958375 821035 945273 128460 896660 018252 848796 426165 > 3¹³⁴ [i]