MinT - Best Known (228−78, 228, s)-Nets in Base 3

Best Known (228−78, 228, s)-Nets in Base 3

(228−78, 228, 162)-Net over F₃ — Constructive and digital

Digital (150, 228, 162)-net over F₃, using

8 times m-reduction [i] based on digital (150, 236, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 118, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(228−78, 228, 329)-Net over F₃ — Digital

Digital (150, 228, 329)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−78, 228, 4700)-Net in Base 3 — Upper bound on s

There is no (150, 228, 4701)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 076992 115687 816594 791890 241945 871974 600721 491684 014206 529376 443952 965030 185447 467188 756191 583941 989033 054651 > 3²²⁸ [i]