On arrays with some combinatorial structure Original Research Article

In this paper we consider combinatorial entities called balanced arrays (B-arrays) which are generalizations of orthogonal arrays (O-arrays) and balanced incomplete block designs (BIBDs). We derive some necessary conditions for the existence of such arrays by using some well-known classical inequalities and the number of coincidences a certain column of the B-array has with other columns. We make some observations on the importance of these conditions to B-arrays, and discuss the applications of these arrays to design of experiments.