This paper defines a class of designs which generalise t-designs, resolvable designs, and orthogonal arrays. For the parameters t = 2, k = 3 and λ = 1, the designs in the class consist of Steiner triple systems, Latin squares, and 1-factorisations of complete graphs. For other values of t and k, we obtain t-designs, Kirkman systems, large sets of Steiner triple systems, sets of mutually orthogo...