An Algorithm for Sequentially Constructing Non-Isomorphic Orthogonal Designs and its Applications

We propose an algorithm for sequentially constructing non-isomorphic orthogonal designs (including both regular and non-regular orthogonal designs). An essential element of the algorithm is using minimal column base to reduce the computations for determining isomorphism between any two designs. By using this algorithm, we obtain the complete catalogs of n k (k = 2; : : : ; n 1) two-level orthogonal designs for n = 12; 16, and 20. Based on this result, we study the statistical properties of the designs using the extended word length pattern (EWLP) criterion. The minimum-aberration designs according to this criterion are obtained and provided for practical use. For 20-run designs, we discover two minimum-aberration designs that are not the projections of Hadamard matrices. These designs were not given in the literature previously.