Grant: Discovery Grants Program - Individual

The objective of my research is to determine the existence of combinatorial objects. After recently completing the search for the (22,8,4) balanced incomplete block design, I would like to work on some of the unsolved cased of partial geometries and their associated strongly regular graphs, especially those with less than 100 points The basic technique for enumerating combinatorial objects is a computer-aided backtrack search. Since the unsolved cases on partial geometries are too big to be attacked directly, I will use the technique of assuming an automorphism in order to reduce the size of the problem. These problems have been long outstanding. Their solution would lead to better understanding of the object and to better computational methods.