Boltzmann models from statistical physics combined with methods from analytic combinatorics give rise to efficient algorithms for the random generation of combinatorials objects. This paper proposes an efficient sampler which satisfies the Boltzmann model principle for ordered structures. This goal is achieved using a special operator, named 'box operator'. Under an abstract real-arithmetic computation model, our algorithm is of linear complexity upon free generation ; and for many classical structures, of linear complexity also provided a small tolerance is allowed on the size of the object drawn. The resulting programs make it possible to generate random objects of sizes up to $10^7$ on a standard machine.