MinT - Best Known (34, 56, s)-Nets in Base 4

Best Known (34, 56, s)-Nets in Base 4

(34, 56, 130)-Net over F₄ — Constructive and digital

Digital (34, 56, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 28, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(34, 56, 1892)-Net in Base 4 — Upper bound on s

There is no (34, 56, 1893)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5219 364240 837452 128330 948527 344080 > 4⁵⁶ [i]