MinT - Best Known (185−71, 185, s)-Nets in Base 3

Best Known (185−71, 185, s)-Nets in Base 3

(185−71, 185, 148)-Net over F₃ — Constructive and digital

Digital (114, 185, 148)-net over F₃, using

9 times m-reduction [i] based on digital (114, 194, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 97, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(185−71, 185, 197)-Net over F₃ — Digital

Digital (114, 185, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−71, 185, 2207)-Net in Base 3 — Upper bound on s

There is no (114, 185, 2208)-net in base 3, because

1 times m-reduction [i] would yield (114, 184, 2208)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6251 191708 625277 252631 746183 029044 969709 732852 453018 466921 993821 280273 239157 148264 097409 > 3¹⁸⁴ [i]