Intersection Numbers For Subspace Designs

Intersection numbers for subspace designs are introduced and q-analogs of the Mendelsohn and Kohler equations are given. As an application, we are able to determine the intersection structure of a putative q-analog of the Fano plane for any prime power q. It is shown that its existence implies the existence of a 2-(7, 3, q^4)_q subspace design. Furthermore, several simplified or alternative proofs concerning intersection numbers of ordinary block designs are discussed.

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