Genealogy of t-designs

Abstract Recent years have seen a dramatic increase in existence results for tdesigns with large t, i.e. t ≥ 5. Designs are now known to exist for several thousand parameter sets, mostly constructed by the method of orbiting under a group. This note is a contribution to the classification of these designs by parameters. We take an abstract look at admissible parameter sets in general. We introduce a partial order, reflecting relationships between designs, and we analyse the structure of the resulting posets. The parameter sets of known designs fall in no more than 100 categories, which we call ancestor clans.