MinT - Best Known (224−60, 224, s)-Nets in Base 4

Best Known (224−60, 224, s)-Nets in Base 4

(224−60, 224, 531)-Net over F₄ — Constructive and digital

Digital (164, 224, 531)-net over F₄, using

t-expansion [i] based on digital (163, 224, 531)-net over F₄, using
- 10 times m-reduction [i] based on digital (163, 234, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 78, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(224−60, 224, 576)-Net in Base 4 — Constructive

(164, 224, 576)-net in base 4, using

1 times m-reduction [i] based on (164, 225, 576)-net in base 4, using
- trace code for nets [i] based on (14, 75, 192)-net in base 64, using
  - 2 times m-reduction [i] based on (14, 77, 192)-net in base 64, using
    - base change [i] based on digital (3, 66, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(224−60, 224, 1498)-Net over F₄ — Digital

Digital (164, 224, 1498)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−60, 224, 125592)-Net in Base 4 — Upper bound on s

There is no (164, 224, 125593)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 726 911860 489263 269279 538970 185355 820082 285037 541055 967363 641035 867894 533980 875263 682286 817252 591807 103305 066282 671112 331706 346049 466304 > 4²²⁴ [i]