Abstract
A t-cover of the finite projective space PG(d,q) is a setS of t-dimensional subspaces such that any point of PG(d,q) is contained in at least one element ofS. In Theorem 1 a lower bound for the cardinality of a t-coverS in PG(d,q) is obtained and in Theorem 2 it is shown that this bound is best possible for all positive integers t,d and for any prime-power q.
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References
Beutelspacher, A.: Partial Spreads in Finite Projective Spaces and Partial Designs. Math. Z.145 (1975), 211–229
Dembowski, P.: Finite Geometries. Berlin-Heidelberg-New York, Springer 1968
Koch, G.G.: A Class of Covers for Finite Projective Geometries Which are related to the Design of Combinatorial Filing Systems. J. Combinat. Theory7 (1969), 215–220
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Beutelspacher, A. On t-covers in finite projective spaces. J Geom 12, 10–16 (1979). https://doi.org/10.1007/BF01920229
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DOI: https://doi.org/10.1007/BF01920229