Wilson loops to 20th order numerical stochastic perturbation theory

We calculate perturbative contributions of Wilson loops of various sizes up to order 20 in $SU(3)$ pure lattice gauge theory at different lattice sizes for the Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high orders of the perturbation theory. We observe differences in the behavior of the series as a function of the loop order n. Up to $n=20$ we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. For Wilson loops of moderate sizes the summed series in boosted perturbation theory reach stable plateaus for moderate perturbative order already. The coefficients in the boosted series become much more stable in the result of smoothing the coefficients of the original series effected by the hypergeometric model. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their nonperturbative parts.