MinT - Best Known (172, 172+56, s)-Nets in Base 3

Best Known (172, 172+56, s)-Nets in Base 3

(172, 172+56, 400)-Net over F₃ — Constructive and digital

Digital (172, 228, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 57, 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]

(172, 172+56, 1015)-Net over F₃ — Digital

Digital (172, 228, 1015)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+56, 43334)-Net in Base 3 — Upper bound on s

There is no (172, 228, 43335)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 079918 705799 368275 890072 327068 055592 114349 933108 686016 920654 986958 121906 438057 163856 055780 538187 009237 323209 > 3²²⁸ [i]