MinT - Best Known (57−23, 57, s)-Nets in Base 4

Best Known (57−23, 57, s)-Nets in Base 4

(57−23, 57, 98)-Net over F₄ — Constructive and digital

Digital (34, 57, 98)-net over F₄, using

1 times m-reduction [i] based on digital (34, 58, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 29, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(57−23, 57, 105)-Net over F₄ — Digital

Digital (34, 57, 105)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−23, 57, 1892)-Net in Base 4 — Upper bound on s

There is no (34, 57, 1893)-net in base 4, because

1 times m-reduction [i] would yield (34, 56, 1893)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5219 364240 837452 128330 948527 344080 > 4⁵⁶ [i]