Discrepancy sets and pseudorandom generators for combinatorial rectangles

A common subproblem of DNF approximate counting and derandomizing RL is the discrepancy problem for combinatorial rectangles. We explicitly construct a poly(n)-size sample space that approximates the volume of any combinatorial rectangle in [n]/sup n/ to within o(1) error. The construction extends the previous techniques for the analogous hitting set problem, most notably via discrepancy preserving reductions.