MinT - Best Known (162, 162+76, s)-Nets in Base 4

Best Known (162, 162+76, s)-Nets in Base 4

(162, 162+76, 450)-Net over F₄ — Constructive and digital

Digital (162, 238, 450)-net over F₄, using

6 times m-reduction [i] based on digital (162, 244, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 122, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(162, 162+76, 752)-Net over F₄ — Digital

Digital (162, 238, 752)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+76, 29513)-Net in Base 4 — Upper bound on s

There is no (162, 238, 29514)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195238 314580 521957 777117 394452 115589 670438 955161 084614 608848 308599 460177 094119 172059 776010 561920 232907 560142 591743 112714 996308 692316 713134 856504 > 4²³⁸ [i]