On incomplete orthogonal arrays (Q1068090)

\textit{E. T. Parker} [Proc. Am. Math. Soc. 13, 219-221 (1962; Zbl 0105.015)] remarked that if an incomplete orthogonal array with parameters (1,r,s,k,2) exists then \(s\geq (r-1)k\). As the author shows, this result is easily extended to incomplete orthogonal arrays (1,r,s,k,t) for which \(s\geq (r-t+1)k\). \textit{K. A. Bush} [Ann. Math. Statistics 23, 426-434 (1952; Zbl 0047.017)] showed that, in an incomplete orthogonal array (1,r,s,k,t), if \(s\leq t\), then \(r\leq t+1\), and the author here observes that if \(s| t\), then \(r=t+1\).