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

In article the problem of construction 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. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct $D$-optimal continues designs of experiments. For linear multiple regression with three factors it is constructed five different types of $D$-optimal continues designs of experiments with heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.