MinT - Best Known (158, 158+63, s)-Nets in Base 3

Best Known (158, 158+63, s)-Nets in Base 3

(158, 158+63, 282)-Net over F₃ — Constructive and digital

Digital (158, 221, 282)-net over F₃, using

1 times m-reduction [i] based on digital (158, 222, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 74, 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]

(158, 158+63, 571)-Net over F₃ — Digital

Digital (158, 221, 571)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+63, 15071)-Net in Base 3 — Upper bound on s

There is no (158, 221, 15072)-net in base 3, because

1 times m-reduction [i] would yield (158, 220, 15072)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 927 682476 164367 505281 983857 795440 781157 814438 825197 280334 649328 611312 662449 347339 673294 326735 523622 703745 > 3²²⁰ [i]