On existence and construction of balanced arrays (Q1802130)

This paper is concerned with the existence conditions and construction procedures for balanced arrays \((B\)-arrays) of strength \(t\), with \(s\) levels, and of size \((m\times N)\) where \(m\) is the number of constraints (rows) and \(N\) denotes the number of columns (runs or treatment- combinations) of the \(B\)-arrays. A necessary and sufficient condition for the existence of such \(B\)-arrays is obtained, and the construction of a \(B\)-array with \(t=2\) based on an \((r,\lambda)\) design with mutually balanced nested subdesigns is given. Several illustrative examples add to the clarity of the paper. The paper ends with the mention of some open and unsolved problems.