Studying designs via multisets

A new method to study families of finite sets, in particular t-designs, by studying families of multisets (also called lists) and their relationships with families of sets, is developed. Notion of the tag for a subset defined earlier by one of the authors is extended to a submultiset. A new concept t-(v, k, λ) list design is defined and studied. Basic existence theory for designs is extended to a new set up of list designs. In particular tags are used to prove that signed t-list designs exist whenever necessary conditions are satisfied. The concepts of homomorphisms and block spreading are extended to this new set up. (