exact bounds for (λ, n)–stable 0-1 matrices

Consider a v × v (0, 1) matrix a with exactly k ones in each row and each column. a is (λ, n)–stable, if it does not contain any λ × n submatrix with exactly one 0. if a is (λ, n)–stable, λ, n ≥ 2, then under suitable conditions on a, v ≥ k/n k(n−1)+(λ−2)/λ−2 . the case of equality leads to new and substantive connections with block designs. the previous bound and characterization of (λ, 2)–stable matrices follows immediately as a special case.