A Note on Discrete Factorial Designs of Resolution Five and Seven and Balanced Arrays

In this paper, we consider the use of balanced arrays (B-arrays) in constructing discrete fractional factorial designs (FFD) of resolution \((2u+1)\), with \(u=2\) and \(3\), in which each of the \(m\) factors is at two levels (say, \(0\) and \(1\)), denoted by factorial designs of \(2^m\) series. We make use of the well-known fact that such designs can be realized under certain conditions, by using balanced arrays of strength four and six (with two symbols), respectively. Here, we consider the existence of B-arrays of strength \(t=4\) and \(t=6\), and discuss how the results presented can be used to obtain the maximum value of \(m\) for a given set of treatment-combinations. Also, we provide some illustrative examples in which the currently available \(\max(m)\) values have been improved upon.