Orbits of infinite block designs

Let D be a 2-(v, k, λ) design with k finite. When v is finite it is well known that block-transitivity implies point-transitivity, whereas for infinite designs the relationship between the numbers of point and block orbits is unknown. We find bounds for the number of block and point orbits and provide a combinatorial proof generalising the result of Cameron that a Steiner triple system has at least as many block orbits as point orbits. We generalise some results of Camina on block-transitive designs and find an upper bound for the point rank.