MinT - Best Known (179−52, 179, s)-Nets in Base 4

Best Known (179−52, 179, s)-Nets in Base 4

(179−52, 179, 531)-Net over F₄ — Constructive and digital

Digital (127, 179, 531)-net over F₄, using

1 times m-reduction [i] based on digital (127, 180, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 60, 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]

(179−52, 179, 867)-Net over F₄ — Digital

Digital (127, 179, 867)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−52, 179, 49083)-Net in Base 4 — Upper bound on s

There is no (127, 179, 49084)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 587272 564729 970691 943903 813200 158508 161489 332728 037397 631596 277915 631140 633438 632137 780418 891531 737955 605729 > 4¹⁷⁹ [i]