Constructing 3-designs from spreads and lines (Q1114926)

The author considers a combinatorial structure generalizing a design, which arises from spreads and partial spreads in a finite projective space. In the case that a usual design is obtained, the main theorem becomes the following. A 3-(v,k,\(\lambda)\) design D can be constructed from a t-spread S of \(PG(2t+1,q)\) with \(v=q^{t+1}+1,\) \(k=q+1,\) \(\lambda =(q^{t+1}-1)/(q-1).\) The points of D are the elements of S and the blocks of D are the lines meeting at least three elements of S.