MinT - Best Known (136, 136+56, s)-Nets in Base 3

Best Known (136, 136+56, s)-Nets in Base 3

(136, 136+56, 252)-Net over F₃ — Constructive and digital

Digital (136, 192, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 64, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(136, 136+56, 469)-Net over F₃ — Digital

Digital (136, 192, 469)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+56, 10532)-Net in Base 3 — Upper bound on s

There is no (136, 192, 10533)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 534993 020490 534399 126638 486858 138826 835773 438720 956125 966687 344802 585997 334000 667516 217585 > 3¹⁹² [i]