MinT - Best Known (102, 102+86, s)-Nets in Base 3

Best Known (102, 102+86, s)-Nets in Base 3

(102, 102+86, 80)-Net over F₃ — Constructive and digital

Digital (102, 188, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 94, 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]

(102, 102+86, 122)-Net over F₃ — Digital

Digital (102, 188, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+86, 987)-Net in Base 3 — Upper bound on s

There is no (102, 188, 988)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 514319 932359 389707 915619 367893 152731 571875 352586 130385 524721 124887 712782 641324 677003 262801 > 3¹⁸⁸ [i]