MinT - Best Known (227−68, 227, s)-Nets in Base 3

Best Known (227−68, 227, s)-Nets in Base 3

(227−68, 227, 246)-Net over F₃ — Constructive and digital

Digital (159, 227, 246)-net over F₃, using

1 times m-reduction [i] based on digital (159, 228, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 76, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(227−68, 227, 497)-Net over F₃ — Digital

Digital (159, 227, 497)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−68, 227, 10340)-Net in Base 3 — Upper bound on s

There is no (159, 227, 10341)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 030836 645418 557458 832500 124209 516391 649780 450256 082467 875613 784703 630898 869428 489652 990731 555376 745995 086481 > 3²²⁷ [i]