A (49,16,3,6) strongly regular graph does not exist

Introduction. A strongly regular graph with 49 vertices and degree 16 has parameters (v, k, ¿, µ) = (49, 16, 3, 6). In this paper we show that such a graph cannot exist. Until now it was the smallest (with respect to the number of vertices) feasible strongly regular graph for which existence was not settled. Our result is the second 'ad hoc' non-existence result for strongly regular graphs. Earlier , Wilbrink and Brouwer [2) proved that (57, 14, 1, 4) cannot be the parameter set of a strongiy regular graph. At the moment the smallest unsettled case is (65, 32, 15, 16). See Brouwer and Van Lint [1) for a survey of recent results on strongly regular graphs. The present proof involves counting techniques, enumeration, Iinear algebra and the use of a computer. Although only a Iittle computing time was needed, we could not manage without a computer