General upper bounds on the minimum size of covering designs
A collection of \(k\)-element subsets (called blocks) out of a \(v\)-set such that each \(t\)-subset of the \(v\)-set is contained in at least one block is called a \((v,k,t)\) covering design. The minimum size of a \((v,k,t)\) covering design is denoted by \(C(v,k,t)\). The authors present several constructions that give infinite families of good covering designs, which lead to new upper bounds on \(C(v,k,t)\). These constructions act on covering designs that can be partitioned into covering designs with other parameters (among others, resolvable designs are used), and on \(t\)-wise balanced designs.
scientific article; zbMATH DE number 1295465
scientific article