Resolvable optimal strong partially balanced designs with block size four Original Research Article

We shall refer to a strong partially balanced design image whose b is the maximum number of blocks in all image, as an optimal strong partially balanced design, briefly image. Resolvable strong partially balanced design was first formulated by Wang, Safavi-Naini and Pei in 2001 [Y. Wang, R. Safavi-Naini, D. Pei, Combinatorial characterization of image-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 image. We show that there exists an image for any image or image except image and some possible exceptions.