A good experimental design in a non-parametric framework, such as Gaussian process modelling in computer experiments, should have satisfactory space-filling properties. Minimax-distance designs minimize the maximum distance between a point of the region of interest and its closest design point, and thus have attractive properties in this context. However, their construction is difficult, even in moderate dimension, and one should in general be satisfied with a design that is not too strongly suboptimal. Several methods based on a discretization of the experimental region will be considered, such as the determination of Chebyshev-centroidal Voronoi tessellations obtained from fixed-point iterations of Lloyds' method, and the construction of any-time (nested) suboptimal solutions by greedy algorithms applied to submodular surrogates of the minimax-distance criterion. The construction of design measures that minimize a regularized version of the criterion will also be investigated.