  We generate all the Orthogonal Arrays (OAs) of a given size n and strength t
as the union of a collection of OAs which belong to an inclusion-minimal set of
OAs. We derive a formula for computing the (Generalized) Word Length Pattern of
a union of OAs that makes use of their polynomial counting functions. In this
way the best OAs according to the Generalized Minimum Aberration criterion can
be found by simply exploring a relatively small set of counting functions. The
classes of OAs with 5 binary factors, strength 2, and sizes 16 and 20 are fully
described.
