Improved upper bounds for partial spreads

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Kurz, Sascha:
Improved upper bounds for partial spreads.
Bayreuth , 2016 . - 8 S.

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Abstract

A partial (k-1)-spread} in PG(n-1,q) is a collection of (k-1)-dimensional subspaces with trivial intersection such that each point is covered exactly once. So far the maximum size of a partial (k-1)-spread in PG(n-1,q) was know for the cases where n is congruent to 0 or 1 modulo k, and for the special case where n is congruent to 2 modulo k, but we additionally have q=2 and k=3. We completely resolve the case where n is congruent to 2 modulo k and q=2, i.e., the binary case.