Genuinely multipartite quantum entanglement and orthogonal arrays

We present a link between the combinatorial notion of orthogonal arrays and k-uniform states, i.e., multipartite pure states such that every reduction to k parties is maximally mixed. As consequence, simple constructions of 1 and 2 uniform states for homogeneous (N qudits) and heterogeneous systems (e.g. N qubits + M qutrits) are derived.