2 problems

Let $H$ be a hyperplane of ${\rm PG}(r+1,q)$, and let an affine vector space partition be a set of subspaces not contained in $H$ such that every point outside $H$ lies in exactly…

Let $v=tk+r$ with integers $t\geq 2$ and $1\leq r\leq k-1$, and let $\mathcal{S}$ be a partial $k$-spread in $\mathbb{F}_q^v$. Its deficiency is the number of points not covered by…