MinT - Best Known (66, 66+58, s)-Nets in Base 4

Best Known (66, 66+58, s)-Nets in Base 4

(66, 66+58, 90)-Net over F₄ — Constructive and digital

Digital (66, 124, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 62, 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]

(66, 66+58, 118)-Net over F₄ — Digital

Digital (66, 124, 118)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+58, 1436)-Net in Base 4 — Upper bound on s

There is no (66, 124, 1437)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 457 824258 313672 860558 709466 596780 651720 014466 550009 663011 902092 235845 131540 > 4¹²⁴ [i]