MinT - Best Known (175, 175+74, s)-Nets in Base 3

Best Known (175, 175+74, s)-Nets in Base 3

(175, 175+74, 264)-Net over F₃ — Constructive and digital

Digital (175, 249, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 83, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(175, 175+74, 554)-Net over F₃ — Digital

Digital (175, 249, 554)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+74, 11869)-Net in Base 3 — Upper bound on s

There is no (175, 249, 11870)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63580 260234 964283 716485 600720 932967 976283 654301 855868 719065 825928 054517 141921 014592 674181 314225 772772 778667 017099 149717 > 3²⁴⁹ [i]