CONSTRUCTION OF GROUP DIVISIBLE DESIGNS

Given any affine design with parameters v, b, r, k, λ and μ = k2/v and any design with parameters v′, b′, r′, k′, λ′ where r′ = tr for some natural number `t and k′≤r, we construct a group divisible design with parameters v′' = vv′, m = v′, n = v, b′' = vb′, k′' = kk′, r′'= kr′, λ1 = tkλ and λ2 = μλ′. This is applied to some series of designs. As a lemma, we also show that any 0-1-matrix with row sums tr and column sums ≤r may be written as the sum of r 0-1-matrices with row sums t and column sums ≤1. © 1979.