FURTHER RESULTS ON THE EXISTENCE OF LABELED RESOLVABLE BLOCK DESIGNS

摘要

It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman system NKS (2,4; v ) if and only if v ≡0 (mod 12) and v ≥24, except possibly when v =264 or 372.