Testing is an important and expensive part of software and hardware development. Over the recent years, the construction of combinatorial interaction tests rose to play an important role towards making the cost of testing more efficient. Covering arrays are the key element of combinatorial interaction testing and a means to provide abstract test sets. In this paper, we present a family of set-based algorithms for generating covering arrays and thus combinatorial test sets. Our algorithms build upon an existing mathematical method for constructing independent families of sets, which we extend sufficiently in terms of algorithmic design in this paper. We compare our algorithms against commonly used greedy methods for producing 3-way combinatorial test sets, and these initial evaluation results favor our approach in terms of generating smaller test sets.