On an optimum design problem for a statistical experiment

An optimum design problem is studied for a statistical experiment of the regression type, observables being, with statistical errors, values of linear functionals on a linearly parameterized family of measures. With Kiefer's $D$-optimization criterion, this problem is reduced to one of maximization of a multulinear form under two-side restrictions. The structure of the minimal non-degenerated plan is described and an iterative process of its search is constructed.