Existence of optimal strong partially balanced designs

A strong partially balanced designs SPBD(v, b, k; λ, 0) whose b is the maximum number of blocks in all SPBD(v, b, k; A strong partially balanced design SPBD(v, b, k; λ, 0) whose b is the maximum number of blocks in all SPBD(v, b, k; λ, 0), as an optimal strong partially balanced design, briefly OSPBD(v, k, λ) is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD(v, k, 1) for k = 3 and 4, and shows that there exists an OSPBD(v, k, 1) for any v, k, 0), as an optimal strong partially balanced design, briefly OSPBD(v, k, λ) is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD(v, k, 1) for k = 3 and 4, and shows that there exists an OSPBD(v, k, 1) for any v = k. © Editorial Committee of Applied Mathematics 2007.