Fedorov (Theory of Optimal Experiments (1972)) gives a sequence of designs converging to a $D$-optimal design. Several modifications of that sequence are given to improve the speed of convergence. The analogous sequence for estimating some of the parameters is shown to converge to a $D$-optimal design, whether or not all the parameters are estimable under the limiting design. We prove the result $d(x, \xi)\xi(x) \leqq 1$, and several related results.
"Sequences Converging to $D$-Optimal Designs of Experiments." Ann. Statist. 1 (2) 342 - 352, March, 1973. https://doi.org/10.1214/aos/1176342371