Let \(B_ n=\{z\in {\mathbb{C}}^ n;| z| <1\}\) be the unit ball of \({\mathbb{C}}^ n\). If f is a holomorphic function of bounded mean oscillation in \(B_ n\), then it has radial limits at almost every point of the boundary \(\partial B_ n\). It was shown that there exists a holomorphic function of bounded mean oscillation with radial limits at no point of the n-torus \(T_ n=\{z\in \partial B_ n,| z_ j| <1/\sqrt{n}\}\). The author shows that this is not an isolated phenomenon; there exists at least one other n-dimensional submanifold of \(\partial B_ n\) with this same behavior.