There is no strongly regular graph with parameters (105,52,21,30)

We prove that no strongly regular graph with parameters (105,52,21,30) exists; the existence of such a graph was listed as open in Brouwer's tables. No symmetry is assumed. Via the Gram matrix −A + 2I + 2J the vertices span an even lattice of rank 21, and the dual vectors of a maximal even overlattice N obey a counting lemma which forbids every norm m/26 with 1 ≤ m ≤ 43, m ≠ 33. The discriminant form of N has determinant 26 or 338, and gluing embeds N into one of the 49 unit-free odd unimodular lattices of dimension 23. In determinant 26, each of the 291 possible hosts contains an exactly verified dual vector of forbidden norm. In determinant 338, an identity between the roots and the characteristic vectors of norm 7, valid for every such lattice and proved with modular forms, excludes 46 of the 49 lattices; two independently written exhaustive enumerations with exact completeness certificates exclude two more; and the shorter Leech lattice is excluded by a short argument in the Leech lattice. The proof is computer-assisted: all hand arguments are given, and every computation is exact or certified by exact counts.