MinT - Best Known (62, 62+50, s)-Nets in Base 4

Best Known (62, 62+50, s)-Nets in Base 4

(62, 62+50, 130)-Net over F₄ — Constructive and digital

Digital (62, 112, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 56, 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]

(62, 62+50, 1669)-Net in Base 4 — Upper bound on s

There is no (62, 112, 1670)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27 295613 611020 678063 538198 844140 834038 398420 038619 272173 308535 790672 > 4¹¹² [i]