Projective (2n,n,λ,1)-designs

A projective (2n,n,λ,1)-design is a set $\text{D}$ of n element subsets (called blocks) of a 2n-element set V having the properties that each element of V is a member of λ blocks and every two blocks have a non-empty intersection. This paper establishes existence and non-existence results for various projective (2n,n,λ,1)-designs and their subdesigns.     

Some remarks on subdesigns of symmetric designs

Let D(υ, k, λ) be a symmetric design containing a symmetric design D₁(υ₁, k₁, λ₁) (k₁ < k) and let x = υ₁(k ? k₁)/(υ ? υ₁). We show that k ≥(k₁ ? x)² + λ If equality holds, D₁ is called a tight subdesign of D. In the special case, λ₁ = λ, the inequality reduces to that of R.C. Bose and S.S. Shrikhande and tight subdesigns then correspond to their notion of Baer subdesigns. The possibilities for (7upsi;, k, λ) designs having Baer subdesigns are investigated.