If the number of runs in a (mixed-level) orthogonal array of strength 2 is specified, what numbers of levels and factors are possible? The collection of possible sets of parameters for orthogonal arrays with N runs has a natural lattice structure, induced by the “expansive replacement” construction method. In particular the dual atoms in this lattice are the most important parameter sets, since...

We develop and apply combinatorial algorithms for investigation of the feasible distance distributions of binary orthogonal arrays with respect to a point of the ambient binary Hamming space utilizing constraints imposed from the relations between the distance distributions of connected arrays. This turns out to be strong enough and we prove the nonexistence of binary orthogonal arrays of param...

A new construction for orthogonal arrays of strength 3 is given.

We prove that binary orthogonal arrays of strength 8, length 12 and cardinality 1536 do not exist. This implies the nonexistence of arrays of parameters (strength,length,cardinality) = (n, n + 4, 6.2) for every integer n ≥ 8.