Balanced arrays of strength two and nested (r, λ)‐designs

An ( r ,λ)‐design with mutually balanced nested subdesigns (for brevity, ( r ,λ)‐design with MBN) is introduced firstly in this article. It is shown that an r ,λ‐design with MBN is equivalent to a balanced array of strength 2 with s symbols. By the use of a nested design and an orthogonal array, a construction of an r ,λ‐design with MBN is given. A direct construction of such an ( r ,λ)‐design, based on the result obtained by Wilson [15], is also given. By these constructions, new balanced arrays with s ≥ 3 are presented. © 1994 John Wiley & Sons, Inc.