MinT - Best Known (96−36, 96, s)-Nets in Base 4

Best Known (96−36, 96, s)-Nets in Base 4

(96−36, 96, 130)-Net over F₄ — Constructive and digital

Digital (60, 96, 130)-net over F₄, using

12 times m-reduction [i] based on digital (60, 108, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 54, 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]

(96−36, 96, 197)-Net over F₄ — Digital

Digital (60, 96, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−36, 96, 4078)-Net in Base 4 — Upper bound on s

There is no (60, 96, 4079)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6302 457655 749378 804786 758450 913976 017059 446335 933899 955058 > 4⁹⁶ [i]