MinT - Best Known (136, 136+103, s)-Nets in Base 3

Best Known (136, 136+103, s)-Nets in Base 3

(136, 136+103, 128)-Net over F₃ — Constructive and digital

Digital (136, 239, 128)-net over F₃, using

7 times m-reduction [i] based on digital (136, 246, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 123, 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]

(136, 136+103, 177)-Net over F₃ — Digital

Digital (136, 239, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+103, 1622)-Net in Base 3 — Upper bound on s

There is no (136, 239, 1623)-net in base 3, because

1 times m-reduction [i] would yield (136, 238, 1623)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 361839 188491 601830 859123 828658 872923 622194 736917 723654 562542 354050 091656 182851 868715 599171 102213 655099 434506 495227 > 3²³⁸ [i]