Groups with maximal irredundant covers and minimal blocking sets

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Let n be a positive integer. Denote by PG(n,q) the n-dimensional projective space over the finite field Fq of order q. A blocking set in PG(n,q) is a set of points that has non-empty intersection with every hyperplane of 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 PG(nᵢ,q) contains a minimal blocking set of size kᵢ for i∈{1,2}, then PG(n₁+n₂+1,q) contains a minimal blocking set of size k₁+k₂-1. This result is proved by a result on groups with maximal irredundant covers.