Design theory
On existence of t-designs with large v and λ
SIAM Journal on Discrete Mathematics
A diagonal form for the incidence matrices of t-subsets vs. k-subsets
European Journal of Combinatorics
A construction for orthogonal arrays with strength t≥3
Discrete Mathematics
A construction for Steiner 3-designs
Journal of Combinatorial Theory Series A
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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, 驴) 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.