PAIRWISE BALANCED DESIGNS WITH BLOCK SIZES 5T + 1

In this paper we construct pairwise balanced designs (PBDs) having block sizes which are prime powers congruent to 1 modulo 5 together with 6. Such a PBD contains n = 5 r + 1 points, for some positive integer r. We show that this condition is sufficient for n greater-than-or-equal-to 1201, with at most 74 possible exceptions below this value. As an application, we prove that there exists an almost resolvable BIB design with n points and block size five whenever n greater-than-or-equal-to 991, with at most 26 possible exceptions below this value.