12 Jul 2016
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Östergård Patric R. J.
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Soicher Leonard H.
We determine that there is no partial geometry ${\cal G}$ with parameters
$(s,t,\alpha)=(4,27,2)$. The existence of such a geometry has been a
challenging open problem of interest to researchers for almost 40 years...The
particular interest in ${\cal G}$ is due to the fact that it would have the
exceptional McLaughlin graph as its point graph. Our proof makes extensive use
of symmetry and high-performance distributed computing, and details of our
techniques and checks are provided. One outcome of our work is to show that a
pseudogeometric strongly regular graph achieving equality in the Krein bound
need not be the point graph of any partial geometry.(read more)