Uniformly resolvable three-wise balanced designs with block sizes four and six
A \(\text{URS}(3,\{4, 6\},v)\) consists of a \(v\)-set and a collection of blocks of size \(4\) or \(6\) such that each \(3\)-subset is contained in a unique block, with the further properties that the set of blocks can be partitioned into parts (called resolution classes) each of which partitions the point set, and that all blocks in a given resolution class are of the same size and so the design is uniform. The authors establish that a \(\text{URS}(3,\{4,6\},v)\) exists if and only if \(v\) is divisible by \(4\). These designs are then used to construct resolvable maximal packings and minimal coverings of triples by quadruples for \(v\) a multiple of \(24\). Results concerning augmented resolvable, and \((1,2)\)-resolvable, Steiner quadruple systems are also obtained.
scientific article; zbMATH DE number 5648207
scientific article