On symplectic semifield spreads of \(\mathrm{PG}(5,q^{2})\), \(q\) odd
This excellent paper yields a classification of semifield symplectic spreads of \(W(5,q^2)\) for \(q\) a large enough odd prime power (n.b., \(q\geqslant 121\)), and having a centre of the associated semifield containing \(\mathbb{F}_q\). The main idea is to exploit the connection between semifield symplectic spreads and certain sets of symmetric matrices known as \textit{spread sets}. These spread sets are in turn associated to linear sets, which are in turn contained in a subspace of a particular quadric Veronesean. There are precisely three such semifield symplectic spreads up to projective equivalence.
scientific article; zbMATH DE number 6859568
scientific article