Improving the accuracy of estimators for the two-point correlation function

We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. We quantify the error of the pair-counts and of the Landy-Szalay estimator by comparing with exact reference values. The standard method, using random point sets, is compared to geometrically motivated estimators and estimators using quasi Monte-Carlo integration. In the standard method the error scales proportional to $1/\sqrt{N_r}$, with $N_r$ the number of random points. In our improved methods the error is scaling almost proportional to $1/N_q$, where $N_q$ is the number of points from a low discrepancy sequence. In an example we achieve a speedup by a factor of $10^4$ over the standard method, still keeping the same level of accuracy. We also discuss how to apply these improved estimators to incompletely sampled galaxy catalogues.