  Let $ (\bx(n))_{n \geq 1} $ be an $s-$dimensional Niederreiter-Xing sequence
in base $b$. Let $D((\bx(n))_{n = 1}^{N})$ be the discrepancy of the sequence $
(\bx(n))_{n = 1}^{N} $. It is known that $N D((\bx(n))_{n = 1}^{N}) =O(\ln^s
N)$ as $N \to \infty $.
  In this paper, we prove that this estimate is exact. Namely, there exists a
constant $K>0$, such that
  $$
  \inf_{\bw \in [0,1)^s} \sup_{1 \leq N \leq b^m} N D((\bx(n)\oplus \bw)_{n =
1}^{N}) \geq K m^s \quad {\rm for} \; \; m=1,2,...\;.
  $$ We also get similar results for other explicit constructions of $(t,s)$
sequences.
