Maximal partial spreads and translation nets of small deficiency

Abstract

Partial t-spreads and translation nets of small deficiency are considered (meaning s > ( d−1) 2, where s is the order and d the deficiency). It is proved that (almost) all such translation nets do in fact come from partial t-spreads and some open questions about the nets belonging to maximal partial t-spreads are answered. Some new examples of maximal partial t-spreads and of unimbeddable nets of small deficiency are also constructed.