Combinatorial Results on Some Balanced Arrays With ${\mu }_2=1$

Abstract

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.