Publication Details

Peter Eades, Peter J. Robinson, Jennifer Seberry Wallis and Ian S. Williams, An algorithm for orthogonal designs, Proceedings of the Fifth Manitoba Conference on Numerical Mathematics, Congressus Numerantium, 15, (1975), 279-292.


Let A =(si) be an n-tuple of positive integers such that Esi = 2k. We give an algorithm which shows that there exists a p = (RA(n, k) - (k+1)) such that there is an orthogonal design of type (2ps1, 2ps2,..., 2psn) in order 2k+p. We evaluate the maximum of p over n-tuples A which add to 2k. Hence we deduce that for any n and k there is an integer q = max RA(n, k) - (k+1) such that for any n-tuple A there is an orthogonal design of type 2qA in order 2q+k.