  The volume of a k-dimensional foliation $\mathcal{F}$ in a Riemannian
manifold $M^{n}$ is defined as the mass of image of the Gauss map, which is a
map from M to the Grassmann bundle of k-planes in the tangent bundle.
Generalizing a construction by Gluck and Ziller, "singular" foliations by
3-spheres are constructed on round spheres $S^{4n+3}$, as well as a singular
foliation by 7-spheres on $S^{15}$, which minimize volume within their
respective relative homology classes. These singular examples provide lower
bounds for volumes of regular 3-dimensional foliations of $S^{4n+3}$ and
regular 7-dimensional foliations of $S^{15}$ .
