Strongly regular graphs on 160, 232, 261 and 280 vertices from fusions of orbitals of PΓL(2,8) and 2^4:(S3×S3)
We construct strongly regular graphs with parameters (160,54,18,18), (232,63,14,18), (261,64,14,16) and (280,63,14,14), and hence also their complements. All four parameter sets were marked "?" (existence unknown) in Brouwer's online table on 11 and 12 October 2026; they are the parameters of the hypothetical partial geometries pg(9,5,3), pg(7,8,2), pg(8,7,2) and pg(9,6,2). We give eight pairwise non-isomorphic graphs: three on 160 vertices, one on 232, two on 261 and two on 280. None of them is geometric. As far as we can determine, they are the first graphs known with these parameters.…
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