MinT - Best Known (224−55, 224, s)-Nets in Base 3

Best Known (224−55, 224, s)-Nets in Base 3

(224−55, 224, 400)-Net over F₃ — Constructive and digital

Digital (169, 224, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 56, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(224−55, 224, 1002)-Net over F₃ — Digital

Digital (169, 224, 1002)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−55, 224, 47621)-Net in Base 3 — Upper bound on s

There is no (169, 224, 47622)-net in base 3, because

1 times m-reduction [i] would yield (169, 223, 47622)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25012 371882 695970 520254 422751 845223 920094 179181 845759 124544 324338 931934 232714 119242 293067 305291 498354 357361 > 3²²³ [i]