MinT - Best Known (176−80, 176, s)-Nets in Base 3

Best Known (176−80, 176, s)-Nets in Base 3

(176−80, 176, 80)-Net over F₃ — Constructive and digital

Digital (96, 176, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 88, 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]

(176−80, 176, 117)-Net over F₃ — Digital

Digital (96, 176, 117)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−80, 176, 952)-Net in Base 3 — Upper bound on s

There is no (96, 176, 953)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 971687 157241 256968 390579 743882 125321 037163 944398 241962 676805 878624 276131 321491 334433 > 3¹⁷⁶ [i]