MinT - Best Known (142, 142+47, s)-Nets in Base 3

Best Known (142, 142+47, s)-Nets in Base 3

(142, 142+47, 328)-Net over F₃ — Constructive and digital

Digital (142, 189, 328)-net over F₃, using

3¹ 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]

(142, 142+47, 829)-Net over F₃ — Digital

Digital (142, 189, 829)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+47, 37420)-Net in Base 3 — Upper bound on s

There is no (142, 189, 37421)-net in base 3, because

1 times m-reduction [i] would yield (142, 188, 37421)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 499864 185235 976203 370852 303559 641685 298314 600490 197378 376505 225198 920423 555478 737172 779707 > 3¹⁸⁸ [i]