MinT - Best Known (136, 136+93, s)-Nets in Base 3

Best Known (136, 136+93, s)-Nets in Base 3

(136, 136+93, 148)-Net over F₃ — Constructive and digital

Digital (136, 229, 148)-net over F₃, using

9 times m-reduction [i] based on digital (136, 238, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 119, 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]

(136, 136+93, 201)-Net over F₃ — Digital

Digital (136, 229, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+93, 2039)-Net in Base 3 — Upper bound on s

There is no (136, 229, 2040)-net in base 3, because

1 times m-reduction [i] would yield (136, 228, 2040)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 117256 357596 616764 013136 012819 959894 302257 586248 415437 003248 680591 470511 262644 693311 516333 888819 816972 915025 > 3²²⁸ [i]