MinT - Best Known (221−65, 221, s)-Nets in Base 3

Best Known (221−65, 221, s)-Nets in Base 3

(221−65, 221, 252)-Net over F₃ — Constructive and digital

Digital (156, 221, 252)-net over F₃, using

1 times m-reduction [i] based on digital (156, 222, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 74, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(221−65, 221, 515)-Net over F₃ — Digital

Digital (156, 221, 515)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−65, 221, 12160)-Net in Base 3 — Upper bound on s

There is no (156, 221, 12161)-net in base 3, because

1 times m-reduction [i] would yield (156, 220, 12161)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 928 363090 289599 543157 158133 336587 684672 233070 670955 652664 092487 458989 827677 011487 961474 905912 621520 027265 > 3²²⁰ [i]