Enumeration of binary orthogonal arrays of strength 1

A k2m×n (0,1) matrix is called a binary orthogonal array of strength m if in any m columns of the matrix every one of the possible 2m ordered (0,1) m-tuples occurs in exactly k rows and no two rows are identical. In this paper, the enumeration of binary orthogonal arrays is studied, and a closed expression for the enumeration of binary orthogonal arrays of strength 1 is given using the inclusion–exclusion principle and the edge-induced subgraph.