MinT - Best Known (164−47, 164, s)-Nets in Base 4

Best Known (164−47, 164, s)-Nets in Base 4

(164−47, 164, 531)-Net over F₄ — Constructive and digital

Digital (117, 164, 531)-net over F₄, using

1 times m-reduction [i] based on digital (117, 165, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 55, 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]

(164−47, 164, 858)-Net over F₄ — Digital

Digital (117, 164, 858)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−47, 164, 58072)-Net in Base 4 — Upper bound on s

There is no (117, 164, 58073)-net in base 4, because

1 times m-reduction [i] would yield (117, 163, 58073)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 136 745258 344809 836824 104155 765968 453177 111410 126800 997487 959430 457993 617027 025813 909545 484086 926040 > 4¹⁶³ [i]