MinT - Best Known (228−66, 228, s)-Nets in Base 3

Best Known (228−66, 228, s)-Nets in Base 3

(228−66, 228, 282)-Net over F₃ — Constructive and digital

Digital (162, 228, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 76, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(228−66, 228, 558)-Net over F₃ — Digital

Digital (162, 228, 558)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−66, 228, 12993)-Net in Base 3 — Upper bound on s

There is no (162, 228, 12994)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 089512 050339 723951 016372 623032 865191 523035 942220 189545 388622 523382 741928 971555 856050 547868 773518 452455 210565 > 3²²⁸ [i]