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An Enumeration of Graphical Designs
Let denote the set of pairs for which there exists
a graphical - design. Most results on graphical designs have
gone to show the finiteness of when and satisfy certain
conditions. The exact determination of for specified and is
a hard problem and only , , , , and
have been determined. In this paper, we determine completely the
sets and . As a result, we find more than 270000
inequivalent graphical designs, and more than 8000 new parameter sets for which
there exists a graphical design. Prior to this, graphical designs are known for
only 574 parameter sets.Comment: 16 page