  Quasi-Monte Carlo algorithms are studied for designing discrete
approximations of two-stage linear stochastic programs. Their integrands are
piecewise linear, but neither smooth nor lie in the function spaces considered
for QMC error analysis. We show that under some weak geometric condition on the
two-stage model all terms of their ANOVA decomposition, except the one of
highest order, are smooth. Hence, Quasi-Monte Carlo algorithms may achieve the
optimal rate of convergence $O(n^{-1+\delta})$ with $\delta \in(0,\frac{1}{2}]$
and a constant not depending on the dimension. The geometric condition is shown
to be generically satisfied if the underlying distribution is normal. We
discuss sensitivity indices, effective dimensions and dimension reduction
techniques for two-stage integrands. Numerical experiments show that indeed
convergence rates close to the optimal rate are achieved when using randomly
scrambled Sobol' point sets and randomly shifted lattice rules accompanied with
suitable dimension reduction techniques.
