Abstract
Let psi(t, k) denote the set of pairs (nu, lambda) for which there exists a graphical t-(nu, k, lambda) design. Most results on graphical designs have gone to show the finiteness of psi(t, k) when t and k satisfy certain conditions. The exact determination of psi(t, k) for specified t and k is a hard problem and only psi(2, 3), psi(2, 4), psi(3, 4), psi(4, 5), and psi(5, 6) have been determined. In this article, we determine completely the sets psi(2, 5) and psi(3, 5). As a result, we find more than 270,000 inequivalent graphical designs, and more than 8,000 new parameter sets for which there exists a graphical design. Prior to this, graphical designs are known for only 574 parameter sets. (C) 2007 Wiley Periodicals, Inc.