The minimum size of a finite subspace partition (Q551275)

Let \(\sigma_q(n,t)\) denote the minimal size in a subspace partition of \(PG(n,q)\) in which the largest subspace has dimension \(t\). In this paper it is proved that \(\sigma_q(n,t)=q^{t+1}+1\) for \(n<2t+2\) and \(\sigma_q(2t+2,t)=q^{t+2}+q^{[t/2]+1}+1\) (Corollary 7). Moreover, the minimal size of a maximal partial \(t\)-spread in \(PG(3t+2,q)\) is given by \(\sigma_q(2t+2,t)\) (Theorem 11).