On the discrepancy of combinatorial rectangles
Let B-d(n) denote the family which consists of all subsets S-1 X...X S-d, where S-i subset of or equal to [n], and S-i not equal circle divide, for i = 1,...,d. We compute the L-2-discrepancy of B-n(d) and give estimates for the L-p-discrepancy of B-n(d) for 1 less than or equal to p less than or equal to infinity. (C) 2002 Wiley Periodicals, Inc.
discrepancy probabilistic method