Olof Heden, in his work "A survey of the different types of vector space partitions", discusses various results regarding the following qustion  given a vector space $V$ over a finite field, how can we partition it into a set $\mathcal P$ of vector spaces, such that every $v\in V,v\ne 0$ belongs to exactly one member of $\mathcal P$? I'm interseted in a generalization of this work to covering any general subset of a vector space over a finite field by not only vector spaces, but also affine spaces. Is anyone familiar with a work done on this subject?
