Designs in Product Association Schemes

Recently, P.J. Cameron studied a class of block designs which generalises the classes of t-designs, -resolved 2-designs, orthogonal arrays, and other classes of combinatorial designs. In fact, Cameron's generalisation of t-designs (when there are no repeated blocks) is a special case of the "poset t-designs" in product association schemes studied ten years earlier by W.J. Martin, who further studied the special case of "mixed block designs". In this paper, we study Cameron's generalisation of t-designs from the point of view of classical t-design theory, in particular investigating the parameters of these generalised t-designs. We show that the t-design constants i (the number of blocks containing an i-subset of the points, where i t) and j i (the number of blocks containing an i-subset I of the points and disjoint from a j-subset J of the points, where I J = and i + j t) have very natural counterparts for generalised t-designs. Our main result places...

• Type: Journal
• Year: 1999
• Where: DCC
• Authors: William J. Martin
• Keywords: Block Designs, Computer Graphics, DCC 1999, Mixed Block Designs, Special Case