Combinatorial Results on Some Balanced Arrays With \(\mu_2=1\)

In this paper, we obtain results on the number of constraints \(m\) for some balanced arrays of strength \(4\) when the parameters \(\mu_2\), \(\mu_3\) assume the values \(1\) and \(0\) respectively. It is shown that the maximum value of \(m\) is \(\mu_1 + 4\), and the existence of such an array is established.