Almost Desarguesian maximal partial spreads (Q5931256)

The authors construct various classes of maximal partial spreads (i.e., maximal sets of pairwise disjoint lines) in \(PG(3,q)\), where \(q=2^r\), with degree \(1+q^2/2\) (and hence with deficiency \(q^2/2\)). Their examples consist of \(q/2\) reguli sharing a line. As an application, they also obtain corresponding classes of maximal partial flocks consisting of \(q/2\) conics.