MinT - Best Known (171, 171+65, s)-Nets in Base 4

Best Known (171, 171+65, s)-Nets in Base 4

(171, 171+65, 531)-Net over F₄ — Constructive and digital

Digital (171, 236, 531)-net over F₄, using

10 times m-reduction [i] based on digital (171, 246, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 82, 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]

(171, 171+65, 1380)-Net over F₄ — Digital

Digital (171, 236, 1380)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+65, 112469)-Net in Base 4 — Upper bound on s

There is no (171, 236, 112470)-net in base 4, because

1 times m-reduction [i] would yield (171, 235, 112470)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3048 704161 028228 717547 702602 500980 385461 484223 714829 065772 389872 106199 640078 320854 132797 784942 603062 147245 346952 152857 397401 954219 108754 516954 > 4²³⁵ [i]