MinT - Best Known (172, 172+74, s)-Nets in Base 3

Best Known (172, 172+74, s)-Nets in Base 3

(172, 172+74, 252)-Net over F₃ — Constructive and digital

Digital (172, 246, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 82, 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]

(172, 172+74, 527)-Net over F₃ — Digital

Digital (172, 246, 527)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+74, 10855)-Net in Base 3 — Upper bound on s

There is no (172, 246, 10856)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2360 574868 749359 174332 395099 264263 349999 628704 697172 609498 832436 080955 252528 927650 923177 554539 598291 359048 192094 737489 > 3²⁴⁶ [i]