Partial spreads over \({\mathbb{Z}}_ q\) (Q1118158)

Let \(G={\mathbb{Z}}_ q^{2n}\) where \(q=p^ a\) and p is a prime. If \(U_ 1,...,U_ r\) is a partial spread, then each \(U_ i\) is isomorphic to \({\mathbb{Z}}^ n_ q\). The author represents partial spreads in G by invertible \(n\times n\) matrices over \({\mathbb{Z}}_ q\). As main result he gets that the maximal size of a spread in \({\mathbb{Z}}_ q^{2n}\) is precisely \(p^ n+1\).