Covering arrays are a relaxation of orthogonal arrays to covering hypothesis that have been successfully applied in the design of test suites for testing systems such as software, circuits and networks, where failures can be caused by the interaction between their parameters.
A covering array t − CA(n, k, g), of size n, strength t, degree k, and order g, is a k × n array on g symbols such that every t × n sub-array contains every t × 1 column on g symbols at least once.
This talk will provide necessary background related to this topic and describe the algebraic construction for strength for covering arrays which we used to improve some best known upper bounds on covering array number.
The second half of the talk will consider a generalization of covering array called covering array on graphs and try
to mention relation between certain graph products like cartesian, direct, strong and their corresponding covering arrays.