On the lower bound of the discrepancy of Halton's sequence
  Let $ (H_s(n))_{n \geq 1} $ be an $s-$dimensional Halton's sequence. Let $D_N$ be the discrepancy of the sequence $ (H_s(n))_{n = 1}^{N} $. It is known that $ND_N =O(\ln^s N)$ as $N \to \infty $.   In this paper we prove that this estimate is exact:   $$   \overline{\lim}_{ N \to \infty} N \ln^{-s}(N) D_N >0.   $$ 
Mordechay B. Levin
math.NT