When designing screening experiments for many factors, two problems quickly arise. The first is that testing all the different combinations of the factors and interactions creates an experiment that is too large to conduct in a practical amount of time. One way this problem is solved is with a combinatorial design called a locating array (LA) which can efficiently identify the factors and interactions most influential on a response. The second problem is how to ensure that combinations that prohibit some particular tests are absent, a requirement that is common in real-world systems. This research proposes a solution to the second problem using constraint satisfaction.