Abstract
Packings (resolutions) of designs have been of interest to combinatorialists in recent years as a way of creating new designs from old ones. Line packings of projective 3-space were the first packings studied, but it is still unknown when a partial packing can be completed to a packing in this case. In this paper we show that there is no guarantee from a combinatorial point of view of completing such a partial packing even when the deficiency is 2. In particular, we construct for every odd prime power q a set of 2(q2+1) lines which doubly cover the points of PG(3,q) and yet cannot be partitioned into two spreads (resolution classes). The method is based on manipulations of primitive elements of finite fields.
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