MinT - Best Known (219−91, 219, s)-Nets in Base 3

Best Known (219−91, 219, s)-Nets in Base 3

(219−91, 219, 148)-Net over F₃ — Constructive and digital

Digital (128, 219, 148)-net over F₃, using

3 times m-reduction [i] based on digital (128, 222, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 111, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(219−91, 219, 182)-Net over F₃ — Digital

Digital (128, 219, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−91, 219, 1761)-Net in Base 3 — Upper bound on s

There is no (128, 219, 1762)-net in base 3, because

1 times m-reduction [i] would yield (128, 218, 1762)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 105 041752 129514 456384 131741 850480 102055 094429 145662 646282 130483 107353 553994 885657 257130 678745 316375 658957 > 3²¹⁸ [i]