MinT - Best Known (159, 159+53, s)-Nets in Base 3

Best Known (159, 159+53, s)-Nets in Base 3

(159, 159+53, 328)-Net over F₃ — Constructive and digital

Digital (159, 212, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 53, 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]

(159, 159+53, 891)-Net over F₃ — Digital

Digital (159, 212, 891)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+53, 39264)-Net in Base 3 — Upper bound on s

There is no (159, 212, 39265)-net in base 3, because

1 times m-reduction [i] would yield (159, 211, 39265)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47058 200639 058478 485989 066139 638969 750630 098599 860298 936301 737223 665983 306758 237291 660382 274616 028073 > 3²¹¹ [i]