MinT - Best Known (70, 132, s)-Nets in Base 4

Best Known (70, 132, s)-Nets in Base 4

(70, 132, 90)-Net over F₄ — Constructive and digital

Digital (70, 132, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 66, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(70, 132, 123)-Net over F₄ — Digital

Digital (70, 132, 123)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 132, 1490)-Net in Base 4 — Upper bound on s

There is no (70, 132, 1491)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30 125923 761791 261785 636943 604929 615718 691921 096951 333893 469800 993911 321407 992832 > 4¹³² [i]