Pair covering designs with block size 5

In this article we look at pair covering designs with a block size of 5 and v = 0 (mod 4). The number of blocks in a minimum covering design is known as the covering number C (v, 5, 2). For v 24, these values are known, and all but v = 8 exceed the Schonheim bound, L(v, 5, 2) = [v/5[(v -1)/4]]. However, for all v >= 28 with v = 0 (mod 4), it seems probable that C(v, 5, 2) L(v, 5, 2). We establish this for all but 17 possible exceptional values lying in the range 40 <= v <= 280. (C) 2006 Elsevier B.V. All rights reserved.