MinT - Best Known (34, 34+26, s)-Nets in Base 4

Best Known (34, 34+26, s)-Nets in Base 4

(34, 34+26, 90)-Net over F₄ — Constructive and digital

Digital (34, 60, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 30, 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]

(34, 34+26, 1124)-Net in Base 4 — Upper bound on s

There is no (34, 60, 1125)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 332656 893519 815179 105741 765975 972176 > 4⁶⁰ [i]