MinT - Best Known (136−40, 136, s)-Nets in Base 3

Best Known (136−40, 136, s)-Nets in Base 3

(136−40, 136, 204)-Net over F₃ — Constructive and digital

Digital (96, 136, 204)-net over F₃, using

3¹ times duplication [i] based on digital (95, 135, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 45, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(136−40, 136, 343)-Net over F₃ — Digital

Digital (96, 136, 343)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−40, 136, 7270)-Net in Base 3 — Upper bound on s

There is no (96, 136, 7271)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77552 466823 758697 891641 668523 222316 093927 793159 426302 136242 600281 > 3¹³⁶ [i]