Number theoryOn the lower bound of the discrepancy of Halton's sequence ISur la limite inferieure de la discrepance de la suite de Halton I
Let (Hs(n))n>=1 be an s dimensional Halton's sequence. Let DN be the discrepancy of the sequence (Hs(n))n=1N. It is known that NDN=O(lnsN) as N In this paper, we prove that this estimate is exact: lim N Nln s(N)DN>0.