We specify an algorithm to enumerate a minimum complete set of combinatorially non-isomorphic orthogonal arrays of given strength t, run-size N, and level-numbers of the factors. The algorithm is the first one handling general mixed-level and pure-level cases. Using an implementation in C, we generate most non-trivial series for t = 2, N ≤ 28, t = 3, N ≤ 64, and t = 4, N ≤ 168. The exceptions define limiting run-sizes for which the algorithm returns complete sets in a reasonable amount of time. q
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