MinT - Best Known (57−24, 57, s)-Nets in Base 4

Best Known (57−24, 57, s)-Nets in Base 4

(57−24, 57, 90)-Net over F₄ — Constructive and digital

Digital (33, 57, 90)-net over F₄, using

1 times m-reduction [i] based on digital (33, 58, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 29, 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]

(57−24, 57, 91)-Net over F₄ — Digital

Digital (33, 57, 91)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−24, 57, 1267)-Net in Base 4 — Upper bound on s

There is no (33, 57, 1268)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 20957 366169 245173 981842 168501 519100 > 4⁵⁷ [i]