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

Balanced nested designs and balanced arrays

“…In this paper we will call it a symmetric balanced nested (r; )-design. In [18], Kuriki and Fuji-Hara not only considered the constructions for symmetric balanced nested (r; )designs, but also established an equivalence between such a design and a balanced array of strength 2, as Theorem 1.3 shows. A generalization of Theorem 1.3 to balanced arrays of strength t is given by Fuji-Hara and Kuriki [12].…”

“…The notion of a balanced array was ÿrst introduced by Chakravarti [7] in connection with some class of statistical designs. Later on, many people contributed to the theory and construction of balanced arrays; see, for example, [8,12,18,22].…”

“…It can be easily veriÿed that (V; B) forms a balanced incomplete block design over V = Z 5 ∪ {∞}, with block size k = 4, and = 12. We partition each block of B into 3 subblocks of size 2; 1 and 1, respectively, to ob- Kuriki and Fuji-Hara [18] deÿned a special class of symmetric balanced nested designs. In each of such designs, the base design (V; B) and the subdesigns (V; B i ) are an (r; )-design and (r i ; i )-designs, respectively, by recalling that i = ii .…”

“…In each of such designs, the base design (V; B) and the subdesigns (V; B i ) are an (r; )-design and (r i ; i )-designs, respectively, by recalling that i = ii . This design is called in [18] an (r; )-design with mutually balanced nested subdesigns. In this paper we will call it a symmetric balanced nested (r; )-design.…”