MinT - Best Known (212−66, 212, s)-Nets in Base 3

Best Known (212−66, 212, s)-Nets in Base 3

(212−66, 212, 192)-Net over F₃ — Constructive and digital

Digital (146, 212, 192)-net over F₃, using

1 times m-reduction [i] based on digital (146, 213, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 71, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(212−66, 212, 415)-Net over F₃ — Digital

Digital (146, 212, 415)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−66, 212, 7614)-Net in Base 3 — Upper bound on s

There is no (146, 212, 7615)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141690 034713 837934 073993 151219 377679 824092 115241 489205 656326 125846 705173 066924 606832 209671 554420 095807 > 3²¹² [i]