MinT - Best Known (224−52, 224, s)-Nets in Base 3

Best Known (224−52, 224, s)-Nets in Base 3

(224−52, 224, 600)-Net over F₃ — Constructive and digital

Digital (172, 224, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 56, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(224−52, 224, 1262)-Net over F₃ — Digital

Digital (172, 224, 1262)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−52, 224, 68027)-Net in Base 3 — Upper bound on s

There is no (172, 224, 68028)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75036 455659 459190 864368 970797 785247 187626 126362 239992 217782 429430 708626 074019 846603 409272 904431 979398 490505 > 3²²⁴ [i]