  Let $n$ be a positive integer. Denote by $\mathrm{PG}(n,q)$ the
$n$-dimensional projective space over the finite field $\mathbb{F}_q$ of order
$q$. A blocking set in $\mathrm{PG}(n,q)$ is a set of points that has non-empty
intersection with every hyperplane of $\mathrm{PG}(n,q)$. A blocking set is
called minimal if none of its proper subsets are blocking sets. In this note we
prove that if $\mathrm{PG}(n_i,q)$ contains a minimal blocking set of size
$k_i$ for $i\in\{1,2\}$, then $\mathrm{PG}(n_1+n_2+1,q)$ contains a minimal
blocking set of size $k_1+k_2-1$. This result is proved by a result on groups
with maximal irredundant covers.
