MinT - Best Known (52, 52+25, s)-Nets in Base 4

Best Known (52, 52+25, s)-Nets in Base 4

(52, 52+25, 195)-Net over F₄ — Constructive and digital

Digital (52, 77, 195)-net over F₄, using

1 times m-reduction [i] based on digital (52, 78, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 26, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(52, 52+25, 291)-Net over F₄ — Digital

Digital (52, 77, 291)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+25, 11453)-Net in Base 4 — Upper bound on s

There is no (52, 77, 11454)-net in base 4, because

1 times m-reduction [i] would yield (52, 76, 11454)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5713 780035 634394 019690 754975 178657 031868 383715 > 4⁷⁶ [i]