MinT - Best Known (178, 178+50, s)-Nets in Base 3

Best Known (178, 178+50, s)-Nets in Base 3

(178, 178+50, 688)-Net over F₃ — Constructive and digital

Digital (178, 228, 688)-net over F₃, using

trace code for nets [i] based on digital (7, 57, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(178, 178+50, 1610)-Net over F₃ — Digital

Digital (178, 228, 1610)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 178+50, 114247)-Net in Base 3 — Upper bound on s

There is no (178, 228, 114248)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 076412 150189 650862 024698 132591 165705 211122 383735 460415 237930 984735 528604 459165 214322 154962 658779 135193 197841 > 3²²⁸ [i]