MinT - Best Known (52, 52+43, s)-Nets in Base 4

Best Known (52, 52+43, s)-Nets in Base 4

(52, 52+43, 90)-Net over F₄ — Constructive and digital

Digital (52, 95, 90)-net over F₄, using

1 times m-reduction [i] based on digital (52, 96, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 48, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(52, 52+43, 105)-Net over F₄ — Digital

Digital (52, 95, 105)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+43, 1416)-Net in Base 4 — Upper bound on s

There is no (52, 95, 1417)-net in base 4, because

1 times m-reduction [i] would yield (52, 94, 1417)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 396 499218 073562 133249 337092 646898 725228 031884 944622 670848 > 4⁹⁴ [i]