ON BALANCED n-ARY t-DESIGNS

A t-(v,k,λ)design(X,B)is a set X of points,of cardinality v,and a collection B of k-subsets of X called blocks,with the property that every t-subset of X is contained in precisely λ blocks.A t-design is a t-(v,k,λ) design for some v,k,γ.In this paper,we give a generalization of t-design called balanced n-ary t-design,and obtain some properties of the new combinatorial structure.

A t-(v, k, λ) design ( X, B ) is a set X of points, of cardinality v, and a collection B of k-subsets of X called blocks, with the property that every t-subset of X is contained in precisely A blocks. A t-design is a t- ( v, k, γ) design for some v, k, γ. In this paper, we give a generalization of t-design called balanced n-ary t-design, and obtain some properties of the new combinatorial structure.