MinT - Best Known (190−47, 190, s)-Nets in Base 3

Best Known (190−47, 190, s)-Nets in Base 3

(190−47, 190, 328)-Net over F₃ — Constructive and digital

Digital (143, 190, 328)-net over F₃, using

3² times duplication [i] based on digital (141, 188, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 47, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(190−47, 190, 850)-Net over F₃ — Digital

Digital (143, 190, 850)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−47, 190, 39252)-Net in Base 3 — Upper bound on s

There is no (143, 190, 39253)-net in base 3, because

1 times m-reduction [i] would yield (143, 189, 39253)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 499663 150459 917410 064189 323733 427152 069113 077931 580152 790944 774429 779739 624589 845367 404891 > 3¹⁸⁹ [i]