MinT - Best Known (74, 74+60, s)-Nets in Base 3

Best Known (74, 74+60, s)-Nets in Base 3

(74, 74+60, 72)-Net over F₃ — Constructive and digital

Digital (74, 134, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 67, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(74, 74+60, 97)-Net over F₃ — Digital

Digital (74, 134, 97)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+60, 785)-Net in Base 3 — Upper bound on s

There is no (74, 134, 786)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8769 385378 506060 799559 102682 124700 269343 331987 459598 811684 173965 > 3¹³⁴ [i]