Double Arrays, Triple Arrays and Balanced Grids with v=r+c −1

Double Arrays, Triple Arrays and Balanced Grids

Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.

Double Arrays, Triple Arrays and Balanced Grids with v=r+c - 1

In Theorem 6.1 of [3] it was shown that, when v = r+ c− 1, every triple array TA(v, k, λrr, λcc, k : r × c) is a balanced grid BG(v, k, k : r×c). Here we prove the converse of this Theorem. Our final result is: Let v = r+ c− 1. Then every triple array is a TA(v, k, c− k, r− k, k : r × c) and every balanced grid is a BG(v, k, k : r × c), and they are equivalent.

Balanced nested designs and balanced arrays

Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric bal...

Cyclic orthogonal and balanced arrays

Kuriki and Fuji-Hara (1994) introduced an (r, 2)-design with mutually balanced nested subdesigns ((r, 2)-design with MBN), which is equivalent to a balanced array of strength 2 with s symbols, and gave some constructions of such (r, 2)-designs. In this paper, we consider cyclic orthogonal and balanced arrays, and we give a cyclic version of the results obtained by them. Furthermore, we give a c...

Paley triple arrays