A strongly regular graph with parameters (288,112,36,48)

We construct a strongly regular graph with parameters (288,112,36,48), and hence one with the complementary parameters (288,175,110,100). Both parameter sets were marked "?" (existence unknown) in Brouwer's online table on 1 November 2026, with the remark that they are the parameters of the point graph of a hypothetical partial geometry pg(7,15,3). The graph has 64+224 vertices: the points of V = F8^2 and the 224 cosets of a cyclic subgroup of order 12 in the affine group K = 2^6:(7:6) of order 2688 generated by the translations of V, the maps (x,y) -> (ax, a^-1 y) (a in F8*), the coordinate swap and the Frobenius map; K is the primitive group PrimitiveGroup(64,7) of the GAP library. Two points of V are adjacent when their difference is non-singular for the quadratic form Tr(xy), and the other adjacencies are given by explicit unions of orbitals of K. The automorphism group is K, with the two vertex orbits of sizes 64 and 224, so the graph is not vertex-transitive and not a Cayley graph. The graph has exactly 64 cliques of size 8 (the Delsarte bound), all of them inside the orbit of size 64; hence it is not geometric, and the existence of pg(7,15,3) remains open. Its clique number is 8 and its independence number is 22 (the Hoffman bound is 36). The graph was found by an exact computer search over unions of orbitals of two-orbit actions of permutation groups of degree 33 to 64; it has been verified by independent programs, and the construction given here regenerates it from the text. The data archive contains the LaTeX source, the graph in graph6 format (also under its search-lane name, and the second, isomorphic, lane solution) with SHA256SUMS, a standalone standard-library SRG verifier, two programs (Python standard library and GAP) that rebuild the graph from its definition and check it, a further standalone GAP construction, the programs for the canonical forms, invariants, clique/coclique numbers and Smith forms, the clean-container run logs, the independent verification report, the referee report and the structure report.