A procedure for finding an improved upper bound on the number of optimal design points

Knowing an upper bound on the number of optimal design points greatly simplifies the search for an optimal design. Carathéodory’s Theorem is commonly used to identify an upper bound. However, the upper bound from Carathéodory’s Theorem is relatively loose when there are three or more parameters in the model. In this paper, an alternative approach of finding a sharper upper bound for classical optimality criteria is proposed. Examples are given to demonstrate how to use the new approach.