MinT - Best Known (177−52, 177, s)-Nets in Base 4

Best Known (177−52, 177, s)-Nets in Base 4

(177−52, 177, 531)-Net over F₄ — Constructive and digital

Digital (125, 177, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 59, 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]

(177−52, 177, 819)-Net over F₄ — Digital

Digital (125, 177, 819)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−52, 177, 44116)-Net in Base 4 — Upper bound on s

There is no (125, 177, 44117)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36703 217916 052074 197822 016900 206095 641028 444558 095048 996780 288567 399748 891937 719473 766229 349950 946557 707312 > 4¹⁷⁷ [i]