MinT - Best Known (34−14, 34, s)-Nets in Base 4

Best Known (34−14, 34, s)-Nets in Base 4

(34−14, 34, 76)-Net over F₄ — Constructive and digital

Digital (20, 34, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 17, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(34−14, 34, 941)-Net in Base 4 — Upper bound on s

There is no (20, 34, 942)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 297 097966 226380 242700 > 4³⁴ [i]