On the star discrepancy of sequences in the unit interval

It is known that there is a constant c>0c>0 such that for every sequence x1,x2,…x1,x2,… in [0,1)[0,1) we have for the star discrepancy DN∗ of the first NN elements of the sequence that NDN∗≥c⋅logN holds for infinitely many NN. Let c∗c∗ be the supremum of all such cc with this property. We show c∗>0.0646363c∗>0.0646363, thereby improving the until now known estimates.