Exact $D$-optimal designs of experiments for linear multiple regression with heteroscedastic observations

In article the problem of construction of exact $D$-optimal designs of experiments for linear multiple regression in a case when variance of errors of observations depend on a point in which is made is investigated. The class functions describing change of variance of heteroscedastic observations is constructed for which exact $D$-optimal designs coincides with exact $D$-optimal designs for homoscedastic observations. The saturated $D$-optimal designs of experiments for linear multiple regression with three factors for heteroscedastic observations are constructed. It is demonstrated that is possible to construct infinite incalculable set of such saturated optimal designs.