Improved Pseudorandom Generators for Combinatorial Rectangles

We construct a pseudorandom generator which uses O(log m + log d + log 3=2 1==) bits and approximates the volume of any combinatorial rectangle in f1; : : : ; mg d to within error. O(log m + log d + log 2 1==) bits. For a subclass of rectangles with at most t log 1== nontriv-ial dimensions and each dimension being an interval, we also give a pseudorandom generator using O(log log d + log 1== log 1=2 t log 1==) bits, which again improves the previous upper bound O(log log d + log 1== log t log 1==)