On existence and number of orthogonal arrays (Q1105609)

The authors show that for significantly large \(\lambda\) an orthogonal array \(A_ t(v,k,\lambda)\) exists for all (v,k,\(\lambda\),t) and that a signed orthogonal array \(SA_ t(v,k,t)\) exists for all (v,k,\(\lambda\),t), \(k\geq t\). As in \textit{N. M. Singhi} and \textit{S. S. Shrikhande} [A reciprocity relation for t-designs, Eur. J. Comb. 8, 59-68 (1987)] a reciprocity relation for the number of distinct orthogonal arrays is derived in the case of designs.