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arxiv: 0912.1503 · v2 · pith:5A77ATSDnew · submitted 2009-12-08 · 🧮 math.CO

q-Analogs for Steiner Systems and Covering Designs

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keywords analogsdesignssteinercoveringsystemsexistenceprovedunknown
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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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