MinT - Best Known (136, 136+105, s)-Nets in Base 3

Best Known (136, 136+105, s)-Nets in Base 3

(136, 136+105, 128)-Net over F₃ — Constructive and digital

Digital (136, 241, 128)-net over F₃, using

5 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+105, 173)-Net over F₃ — Digital

Digital (136, 241, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+105, 1559)-Net in Base 3 — Upper bound on s

There is no (136, 241, 1560)-net in base 3, because

1 times m-reduction [i] would yield (136, 240, 1560)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 261574 447713 500202 830748 531347 701949 433310 743600 635851 537114 146901 851139 187855 177031 630076 013894 834178 548138 998977 > 3²⁴⁰ [i]