MinT - Best Known (188−47, 188, s)-Nets in Base 3

Best Known (188−47, 188, s)-Nets in Base 3

(188−47, 188, 328)-Net over F₃ — Constructive and digital

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]

(188−47, 188, 808)-Net over F₃ — Digital

Digital (141, 188, 808)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−47, 188, 35674)-Net in Base 3 — Upper bound on s

There is no (141, 188, 35675)-net in base 3, because

1 times m-reduction [i] would yield (141, 187, 35675)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 166672 237152 147320 982611 852810 651483 736069 000708 011806 682553 845379 491134 881156 400724 526531 > 3¹⁸⁷ [i]