Constructing -designs from -wise balanced designs

We give a construction for obtaining a t -design from a t -wise balanced design. More precisely, given a positive integer k and a t - ( v , { k 1 , k 2 , … , k s } , λ ) design D , with all block-sizes k i occurring in D and 1 ≤ t ≤ k ≤ k 1 < k 2 < ⋯ < k s , the construction produces a t - ( v , k , n λ ) design D ∗ , with n = lcm ( k 1 − t k − t , … , k s − t k − t ) . We prove that Aut ( D ) is a subgroup of Aut ( D ∗ ) , with equality when both λ = 1 and t < k . We employ our construction in another construction, which, given a t - ( v , k , λ ) design with 1 ≤ t < k < v , and a point of this design, yields a t - ( v − 1 , k − 1 , ( k − t ) λ ) design. Many of the t -designs coming from our constructions appear to be new.