There is no strongly regular graph with parameters (405,132,63,33)

We prove that no strongly regular graph with parameters (405,132,63,33) exists. Brouwer's table lists this parameter set as open, and its complement (405,272,172,204) as the putative point graph of a partial geometry pg(8,33,6); Koolen and Gebremichel list it among the twelve open primitive parameter sets with smallest eigenvalue −3, v > 276 and μ ∉ {6,9}. As a corollary, there is no partial geometry pg(8,33,6). No symmetry is assumed. The matrix A + 3I + J is positive semidefinite of rank 31, so the vertices span an even lattice L of rank 31; let N be a maximal even overlattice. We prove by hand that the discriminant form of N is one of exactly four forms, of orders 4, 12, 12 and 36; the proof combines Milgram's formula with a parity condition satisfied by the class of the normalized sum of the vertex vectors. The key new ingredient is an elementary counting lemma: if R₀ is the set of roots of N and S₄ the set of norm-4 vectors of N having inner product 2 with that normalized sum (as the vertex vectors do), then 36|R₀| ≤ 3(|S₄| − 405). The lemma is sharp on the line graph of PG(4,2). For the discriminant form Z/4⟨7/4⟩, gluing N to ⟨4⟩ gives an even unimodular lattice of rank 32 whose harmonic theta series of degrees ≤ 6 force the identity |S₄| = 171 + 3|R₀|; we print the six equations and the multipliers. Together with the lemma this gives 9|R₀| ≤ −234. The other three forms are excluded by exact rational certificates, by the lemma or by the differences of adjacent vertices. The proof is computer-assisted in the admissibility of a few dozen vector types and in three certificates; the reduction, the list of four forms, the counting lemma and the decisive identity are proved in the text. All certificates are checked by short exact programs (Python, exact rational arithmetic, no linear-programming solver) that run in seconds and are included in the data archive. The result was obtained and checked along independent lines: a derivation; a blind audit by a different model with its own code and no access to the derivation's code (re-derived the form list, the counting lemma and the harmonic systems with two independent row builders); a third, paper-side recomputation of the decisive system from the formulas of the paper; and an independent referee re-implementation (own PARI/GP and Python code) that reproduced the hand proofs, the rows and identities for all four forms, and the planted controls. Each row builder passes a planted control on a real lattice (line graph of PG(4,2)). The paper states exactly which parts are computational and which checks by a human expert are still owed.