Existence of optimal strong partially balanced designs with block size five Original Research Article

We shall refer to a strong partially balanced design SPBD(v,b,k;λ,0) whose b is the maximum number of blocks in any SPBD(v,b,k;λ,0), as a optimal strong partially balanced design, briefly OSPBD(v,k,λ). This article investigates the existence of OSPBD(v,5,1), we show that there exists an OSPBD(v,5,1) for any v≡0,1,3 (mod 4), except v=15 and except possibly v=135.