MinT - Best Known (224−104, 224, s)-Nets in Base 3

Best Known (224−104, 224, s)-Nets in Base 3

(224−104, 224, 80)-Net over F₃ — Constructive and digital

Digital (120, 224, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 112, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(224−104, 224, 136)-Net over F₃ — Digital

Digital (120, 224, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−104, 224, 1098)-Net in Base 3 — Upper bound on s

There is no (120, 224, 1099)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 78446 806347 353177 864815 088430 468322 271285 420955 249485 130904 762506 592912 645579 491806 036475 655845 367768 302969 > 3²²⁴ [i]