MinT - Best Known (136−62, 136, s)-Nets in Base 3

Best Known (136−62, 136, s)-Nets in Base 3

(136−62, 136, 68)-Net over F₃ — Constructive and digital

Digital (74, 136, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 68, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(136−62, 136, 94)-Net over F₃ — Digital

Digital (74, 136, 94)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−62, 136, 739)-Net in Base 3 — Upper bound on s

There is no (74, 136, 740)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79109 202942 990554 296907 020439 728080 682698 578833 158674 755387 278897 > 3¹³⁶ [i]