MinT - Best Known (94, 94+78, s)-Nets in Base 3

Best Known (94, 94+78, s)-Nets in Base 3

(94, 94+78, 80)-Net over F₃ — Constructive and digital

Digital (94, 172, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 86, 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]

(94, 94+78, 115)-Net over F₃ — Digital

Digital (94, 172, 115)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+78, 940)-Net in Base 3 — Upper bound on s

There is no (94, 172, 941)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11723 482798 802609 466530 923597 891661 584652 959839 377549 446285 687399 522905 175864 353019 > 3¹⁷² [i]