MinT - Best Known (96−41, 96, s)-Nets in Base 4

Best Known (96−41, 96, s)-Nets in Base 4

(96−41, 96, 130)-Net over F₄ — Constructive and digital

Digital (55, 96, 130)-net over F₄, using

2 times m-reduction [i] based on digital (55, 98, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 49, 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]

(96−41, 96, 1988)-Net in Base 4 — Upper bound on s

There is no (55, 96, 1989)-net in base 4, because

1 times m-reduction [i] would yield (55, 95, 1989)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1581 585085 086621 242336 430575 098918 130470 545068 458161 721396 > 4⁹⁵ [i]