Binary ( k, k )-Designs

Todorka Alexandrova, Peter Boyvalenkov and Angel Dimitrov
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Todorka Alexandrova: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113 Sofia, Bulgaria
Peter Boyvalenkov: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113 Sofia, Bulgaria
Angel Dimitrov: Department of Mathematics, Technical University Munich, Boltzmannstrasse 3, Garching b. 85748 Munich, Germany

Mathematics, 2020, vol. 8, issue 11, 1-9

Abstract: We introduce and investigate binary ( k , k ) -designs, a special case of T -designs. Our combinatorial interpretation relates ( k , k ) -designs to the binary orthogonal arrays. We derive a general linear programming bound and propose as a consequence a universal bound on the minimum possible cardinality of ( k , k ) -designs for fixed k and n . Designs which attain our bound are investigated.

Keywords: binary ( k , k )-designs; orthogonal arrays; linear programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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