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

A tt-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 vv with block sizes four and six exists if and only if vv 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 vv for v≡0(mod24), augmented resolvable Steiner quadruple systems of order vv for v≡26,58,74(mod96) and (1,2)(1,2)-resolvable Steiner quadruple systems of order vv for v≡74(mod96).