Embedding partial geometries in Steiner designs
We consider the following problem: given a partial geometry with v points and k points on a line, can one add to the line set a set of k-subsets of points such that the extended family of k-subsets is a 2-(v, k;, 1) design (or a Steiner system S(2, k, v)). We give some necessary conditions for such embeddings and several examples. One of these is an embedding of the partial geometry PQ+(7,2) into a 2-(120,8,1) design.
Geometry, Combinatorial Designs and Related Structures
Embedding partial geometries in Steiner designs.
Geometry, Combinatorial Designs and Related Structures, 33-42.
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