Special sets of lines in PG(3, 2) Original Research Article

Using a particular representation, we investigate the sets of lines in PG(3, 2) having the property that every point is incident with the same number n of lines of the set and we determine the orbits of these sets under PSL(4, 2). The main case (n = 3), in particular, has been studied before by Bussemaker and Seidel. While they use a combinatorial approach, ours has a more geometric flavor and may add some new details. In particular, we provide a proof that the five types of sets with n = 3 given by them exhaust all possibilities. We also consider parallelisms.