Applications of algebraic combinatorics to design theory and extremal set-partition theory

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Thorough testing of circuits, software and networks is critical but it is often neglected since it can be complicated and time consuming. Researchers have tried to find testing schemes that would reduce the amount of work required to test a system, while still having a rigorous set of tests. One such scheme is determined by a design called a covering array. A covering array describes a scheme that completely tests every pair of parameters in the system, rather than completely testing all possible sets of parameters in a system. This leads to testing that is both effective and efficient. A further improvement on such a testing scheme is to only test pairs of parameters that are known to interact. Since the set of pairs which interact can be recorded in a graph structure, this leads to a refinement, called a covering array on a graph.