Average case complexity of multivariate integration

We study the average case complexity of multivariate integration for the class of continuous functions of d variables equipped with the classical Wiener sheet measure. To derive the average case complexity one needs to obtain optimal sample points. This optimal design problem has long been open. All known designs guaranteeing average case error e lead to an exponential number of sample points, roughly 6(e~ ). For d large this makes the problem intractable for even the fastest computers.