MinT - Best Known (96−42, 96, s)-Nets in Base 4

Best Known (96−42, 96, s)-Nets in Base 4

(96−42, 96, 130)-Net over F₄ — Constructive and digital

Digital (54, 96, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 48, 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]

(96−42, 96, 1618)-Net in Base 4 — Upper bound on s

There is no (54, 96, 1619)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6313 544234 303245 897736 288791 531789 539187 910078 894337 481312 > 4⁹⁶ [i]