MinT - Best Known (54, 54+41, s)-Nets in Base 4

Best Known (54, 54+41, s)-Nets in Base 4

(54, 54+41, 130)-Net over F₄ — Constructive and digital

Digital (54, 95, 130)-net over F₄, using

1 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+41, 1853)-Net in Base 4 — Upper bound on s

There is no (54, 95, 1854)-net in base 4, because

1 times m-reduction [i] would yield (54, 94, 1854)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 392 334788 723770 609291 255376 168097 112462 169231 748705 623491 > 4⁹⁴ [i]