A fast algorithm of balanced sampling

The cube method (Deville & Tillé 2004) is a large family of algorithms that allows selecting balanced samples with equal or unequal inclusion probabilities. In this paper, we propose a very fast implementation of the cube method. The execution time does not depend on the square of the population size anymore, but only on the population size. Balanced samples can thus be selected in very large populations of several hundreds of thousands of units.