C O ] 2 3 M ar 2 01 0 q-Analogs for Steiner Systems and Covering Designs

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.