In this article, we establish a matrix inequality which shows that the objective function is submodular for all , from which it follows that the greedy approach, which has often been used for this problem, always gives a design within of the optimum. We next study the design found by rounding the solution of the continuous relaxed problem, an approach which has been applied by several authors. We prove an inequality which generalizes a classical result from the theory of optimal designs, and allows us to give a rounding procedure with an approximation factor which tends to 1 as goes to 1.