Exact order of extreme [Formula: see text] discrepancy of infinite sequences in arbitrary dimension

We study the extreme [Formula: see text] discrepancy of infinite sequences in the d-dimensional unit cube, which uses arbitrary sub-intervals of the unit cube as test sets. This is in contrast to the classical star [Formula: see text] discrepancy, which uses exclusively intervals that are anchored in the origin as test sets. We show that for any dimension d and any [Formula: see text] , the extreme [Formula: see text] discrepancy of every infinite sequence in [Formula: see text] is at least of order of magnitude [Formula: see text] , where N is the number of considered initial terms of the sequence. For [Formula: see text] , this order of magnitude is best possible.