MinT - Best Known (62, 62+54, s)-Nets in Base 4

Best Known (62, 62+54, s)-Nets in Base 4

(62, 62+54, 90)-Net over F₄ — Constructive and digital

Digital (62, 116, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 58, 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]

(62, 62+54, 114)-Net over F₄ — Digital

Digital (62, 116, 114)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+54, 1383)-Net in Base 4 — Upper bound on s

There is no (62, 116, 1384)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6915 097894 572672 356985 998460 990365 535184 300272 160355 351277 564960 316540 > 4¹¹⁶ [i]