$q$-Analogs for Steiner Systems and Covering Designs

Details $q$-Analogs for Steiner Systems and Covering Designs $q$-Analogs for Steiner Systems and Covering Designs

2009-12-08

arxiv.org/abs/0912.1503v2

Mathematics

Combinatorics

submitted for ALCOMA10

Scientific paper

The $q$-analogs of basic designs are discussed. It is proved that the
existence of any unknown Steiner structures, the $q$-analogs of Steiner
systems, implies the existence of unknown Steiner systems. Optimal $q$-analogs
covering designs are presented. Some lower and upper bounds on the sizes of
$q$-analogs covering designs are proved.

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