Reliable autofocusing is a critical part of any automated microscopy system: by precisely positioning the sample in the focal plane, the acquired images are sharp and can be accurately segmented and quantified. The three main components of an autofocus algorithm are a contrast function, an optimization algorithm and a sampling strategy. The latter has not been given much attention in the literature. It is however a very important part of the autofocusing algorithm, especially in high content and high throughput image-based screening. It deals with the problem of sampling the focus surface as sparsely as possible to reduce bleaching and computation time while with sufficient detail as to permit a faithful interpolation. We propose a new strategy that has higher performance compared to the classical square grid or the hexagonal lattice, which is based on the concept of low discrepancy point sets and in particular on the Halton point set. We tested the new algorithm on nine different focus surfaces, each under 24 different combinations of Signal-to-Noise ratio (SNR) and sampling rate, obtaining that in 88% of the tested conditions, Halton sampling outperforms its counterparts.