MinT - Best Known (206−61, 206, s)-Nets in Base 4

Best Known (206−61, 206, s)-Nets in Base 4

(206−61, 206, 531)-Net over F₄ — Constructive and digital

Digital (145, 206, 531)-net over F₄, using

1 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 69, 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]

(206−61, 206, 898)-Net over F₄ — Digital

Digital (145, 206, 898)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−61, 206, 52184)-Net in Base 4 — Upper bound on s

There is no (145, 206, 52185)-net in base 4, because

1 times m-reduction [i] would yield (145, 205, 52185)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2645 224193 610294 093499 415412 896707 931878 679034 218298 096311 959019 650264 514495 683539 071542 528556 784362 106510 285956 716856 657440 > 4²⁰⁵ [i]