A uniform bound on a combinatorial central limit theorem for randomized orthogonal array sampling designs

Let X be a uniform random vector on the unit cube [0, 1](3) and f : [0, 1](3) -> IR be a measurable function. In many computer experiments, we would like to estimate the value of integral([0,1]3) f(x)dx, which is E(f circle X), by computing fat a number points in [0, 1](3). There are many ways to choose these points and one of these is randomized orthogonal arrays which was proposed independently by Owen and Tang [10, 18], respectively. In this article, we give a uniform bound on a combinational central limit theorem for the randomized orthogonal arrays sampling designs which are based on OA(q(2), 3, q, 2) by using Stein's method. Our order is O(q(1/2)) which is better than Loh's order [6].