The spectrum of optimal strong partially balanced designs with block size five

We shall refer to a strong partially balanced design S P B D (v, b, k; lambda, 0) whose b is the maximum number of blocks in all S P B D (v, b, k; lambda, 0), as an optimal strong partially balanced design, briefly 0 S P B D (v, k, A). The author in paper (Discrete Math. 279 (2004) 173) investigated the existence of OSPBD(v, 5, 1) and gave the spectra of OSPBD(v, 5, 1) for v equivalent to 0, 1, 3 (mod4). In this article we shall investigate the existence of OSPBD(v, 5, 1) and give the spectrum of OSPBD(v, 5, 1) for the remaining case v equivalent to 2 (mod 4). (C) 2004 Elsevier B.V. All rights reserved.