MinT - Best Known (54, 54+39, s)-Nets in Base 4

Best Known (54, 54+39, s)-Nets in Base 4

(54, 54+39, 130)-Net over F₄ — Constructive and digital

Digital (54, 93, 130)-net over F₄, using

3 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+39, 133)-Net over F₄ — Digital

Digital (54, 93, 133)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+39, 2159)-Net in Base 4 — Upper bound on s

There is no (54, 93, 2160)-net in base 4, because

1 times m-reduction [i] would yield (54, 92, 2160)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24 719608 231837 245606 381136 139564 570387 219033 880354 437758 > 4⁹² [i]