Uniformly resolvable three-wise balanced designs with block sizes four and six

A t -wise balanced design is said to be resolvable if its block set can be partitioned into parts (called resolution classes) such that each part is itself a partition of the point set. It is uniform if all blocks in each resolution class have the same size. In this paper, it is shown that a uniformly resolvable three-wise balanced design of order v with block sizes four and six exists if and only if v is divisible by 4. These uniformly resolvable three-wise balanced designs are also used to construct the infinite classes of resolvable maximal packings (minimal coverings) of triples by quadruples of order v for v ≡ 0 ( mod 24 ) , augmented resolvable Steiner quadruple systems of order v for v ≡ 26 , 58 , 74 ( mod 96 ) and ( 1 , 2 ) -resolvable Steiner quadruple systems of order v for v ≡ 74 ( mod 96 ) .