An Algorithm for Finding Exact D- and A- Optimal Designs with n Observations and k Two-Level Factors in the Presence of Autocorrelated Errors

Exact designs with \(n\) observations and \(k\) two-level factors in the presence of autocorrelated errors are considered. The problem of finding \(D\)- and \(A\)- optimal designs is discussed. An algorithm for constructing such designs, using exhaustive search for different values of \(n\) and \(k\), is developed. The application of this algorithm showed that, in the case of positive autocorrelation, the maximum possible number of interchanges of the factor levels provides almost optimal designs.
On the contrary, in the case of negative autocorrelation, the minimum such number provides almost optimal designs. A list of the exact \(D\)- and \(A\)-optimal designs is given.