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.
