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This article deals with constructions of covering arrays which are extremely useful in software testing in order to guarantee 3-way coverage of parameter values, while trying to minimize the number of test cases. A practical limitation in the realm of testing is budget. In most software development environments, time, computing and human resources needed to perform the testing of a component is strictly limited. In order to deal with such situations, we consider the problem of creating the best possible test suite (covering the maximum number of 3-tuples) within a fixed number of test cases. This paper proposes a method of constructing strength three covering arrays with budget constraints.