MinT - Best Known (89, 123, s)-Nets in Base 4

Best Known (89, 123, s)-Nets in Base 4

(89, 123, 531)-Net over F₄ — Constructive and digital

Digital (89, 123, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 41, 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]

(89, 123, 786)-Net over F₄ — Digital

Digital (89, 123, 786)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 123, 54299)-Net in Base 4 — Upper bound on s

There is no (89, 123, 54300)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 113 096123 225204 267503 697182 567362 950021 364620 324786 156148 258886 691145 727891 > 4¹²³ [i]