MinT - Best Known (146, 146+63, s)-Nets in Base 3

Best Known (146, 146+63, s)-Nets in Base 3

(146, 146+63, 228)-Net over F₃ — Constructive and digital

Digital (146, 209, 228)-net over F₃, using

1 times m-reduction [i] based on digital (146, 210, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 70, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(146, 146+63, 453)-Net over F₃ — Digital

Digital (146, 209, 453)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+63, 9839)-Net in Base 3 — Upper bound on s

There is no (146, 209, 9840)-net in base 3, because

1 times m-reduction [i] would yield (146, 208, 9840)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1743 284258 489007 847475 069926 498909 949504 012925 239153 178645 708833 885191 886419 552753 033216 646944 423233 > 3²⁰⁸ [i]