MinT - Best Known (246−61, 246, s)-Nets in Base 3

Best Known (246−61, 246, s)-Nets in Base 3

(246−61, 246, 328)-Net over F₃ — Constructive and digital

Digital (185, 246, 328)-net over F₃, using

3² times duplication [i] based on digital (183, 244, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 61, 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]

(246−61, 246, 1042)-Net over F₃ — Digital

Digital (185, 246, 1042)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−61, 246, 47421)-Net in Base 3 — Upper bound on s

There is no (185, 246, 47422)-net in base 3, because

1 times m-reduction [i] would yield (185, 245, 47422)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 784 758553 496065 601322 405384 452061 410300 499774 460749 888110 129668 390504 680473 069811 165195 978133 589672 245912 134972 778965 > 3²⁴⁵ [i]