Existence of resolvable optimal strong partially balanced designs ?
We shall refer to a strong partially balanced design SPBD(v,b,k;?,0) SPBD ( v , b , k ; ? , 0 ) whose b  is the maximum number of blocks in all SPBD(v,b,k;?,0) SPBD ( v , b , k ; ? , 0 ) , as an optimal strong partially balanced design, briefly OSPBD(v,k,?) OSPBD ( v , k , ? ) . Resolvable strong partially balanced design was first formulated by Wang, Safavi-Naini and Pei [Combinatorial characterization of l-optimal authentication codes with arbitration, J. Combin. Math. Combin. Comput. 37 (2001) 205224] in investigation of l -optimal authentication codes. This article investigates the existence of resolvable optimal strong partially balanced design ROSPBD(v,3,1) ROSPBD ( v , 3 , 1 ) . We show that there exists an ROSPBD(v,3,1) ROSPBD ( v , 3 , 1 ) for any v?3 v ? 3 except v=6,12 v = 6 , 12 .
resolvable strong partially balanced design kirkman frame