Mutually disjoint Steiner systems S(5, 8, 24) and 5-(24, 12, 48) designs

Abstract

We demonstrate that there are at least 50 mutually disjoint Steiner systems S(5, 8, 24) and there are at least 35 mutually disjoint 5-(24, 12, 48) designs. The latter result provides the existence of a simple 5-(24, 12, 6m) design for m = 24, 32, 40, 48, 56, 64, 72, 80, 112, 120, 128, 136, 144, 152, 160, 168, 200, 208, 216, 224, 232, 240, 248 and 256.