Existence of resolvable optimal strong partially balanced designs

Authors:
Beiliang Du
Affiliations:
Department of Mathematics, Suzhou University, Suzhou 215006, PR China
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

We shall refer to a strong partially balanced design SPBD(v,b,k;@l,0) whose b is the maximum number of blocks in all SPBD(v,b,k;@l,0), as an optimal strong partially balanced design, briefly OSPBD(v,k,@l). 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) 205-224] in investigation of l-optimal authentication codes. This article investigates the existence of resolvable optimal strong partially balanced design ROSPBD(v,3,1). We show that there exists an ROSPBD(v,3,1) for any v=3 except v=6,12.