Lower　bound　estimation　of　the　packing　number　plays　an　important　role　in　matrix　denoising.　By　using　the　metric　entropy　of　the　Grassmannian　manifold,　Cai,　Ma　and　Wu　provide　a　lower　bound　estimation　of　the　packing　number　with　the　metric　based　on　Frobenius　norm,　see　Cai　et　al.　(2013).　In　this　paper,　we　extend　their　result　to　all　metrics　based　on　unitarily　invariant　norms　and　then　give　an　example　to　show　the　optimality　of　our　estimation.　Finally,　we　discuss　a　potential　application　in　low-rank　matrix　denoising.　(C)　2022　Elsevier　B.V.　All　rights　reserved.