MinT - Best Known (147, 147+59, s)-Nets in Base 3

Best Known (147, 147+59, s)-Nets in Base 3

(147, 147+59, 264)-Net over F₃ — Constructive and digital

Digital (147, 206, 264)-net over F₃, using

1 times m-reduction [i] based on digital (147, 207, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 69, 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]

(147, 147+59, 529)-Net over F₃ — Digital

Digital (147, 206, 529)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+59, 13738)-Net in Base 3 — Upper bound on s

There is no (147, 206, 13739)-net in base 3, because

1 times m-reduction [i] would yield (147, 205, 13739)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 581182 267512 911380 221110 876165 293529 213738 323149 103838 160313 919403 116284 153470 689728 047019 846943 > 3²⁰⁵ [i]