New Uniform Subregular Parallelisms of PG(3, 4) Invariant under an Automorphism of Order 2

摘要

A spread in PG(n, q) is a set of lines which partition the point set. Aparallelism is a partition of the set of lines by spreads. A parallelism is uniform if allits spreads are isomorphic. Up to isomorphism, there are three spreads of PG(3, 4)– regular, subregular and aregular. Therefore, three types of uniform parallelismsare possible. In this work, we consider uniform parallelisms of PG(3, 4) whichpossess an automorphism of order 2. We establish that there are no regularparallelisms, and that there are 8253 nonisomorphic subregular parallelisms.Together with the parallelisms known before this work, this yields a total of 8623known subregular parallelisms of PG(3, 4).