Constructing t-designs from t-wise balanced designs

We give a construction to obtain a t-design from a t-wise balanced design. More precisely, given a positive integer k and a t(v, {k1, k2, . . . , ks}, λ) design D, with with all block-sizes ki occurring in D and 1 ≤ t ≤ k ≤ k1 < k2 < · · · < ks, the construction produces a t-(v, k, nλ) design D∗, with n = lcm( k1−t k−t , . . . , ks−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.

• Type: Journal
• Year: 2007
• Where: EJC
• Authors: John P. McSorley, Leonard H. Soicher
• Keywords: Design, EJC 2007, Information Technology, Positive Integer, T-wise Balanced Design