MinT - Best Known (54, 54+30, s)-Nets in Base 4

Best Known (54, 54+30, s)-Nets in Base 4

(54, 54+30, 130)-Net over F₄ — Constructive and digital

Digital (54, 84, 130)-net over F₄, using

12 times m-reduction [i] based on 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]

(54, 54+30, 212)-Net over F₄ — Digital

Digital (54, 84, 212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+30, 5025)-Net in Base 4 — Upper bound on s

There is no (54, 84, 5026)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 375 126116 634360 530393 127188 964426 463202 646491 324944 > 4⁸⁴ [i]