On arrays with some combinatorial structure (Q1842160)

An \(m\times N\) matrix with entries equal to 0 or 1 is called a \(B\)-array of strength \(t\) if in every \(t\times N\) submatrix each vector of weight \(i\) \((0\leq i\leq t)\) occurs \(\mu_ i\) times where \(\mu_ i\) is independent of the submatrix chosen. Here inequalities are established for \(B\)-arrays of strength 4 in terms of the parameters \(\mu_ i\) and \(m\) and the number \(l\) of 1's appearing in a given column. Since the addition of a column of all 1's preserves the property of being a \(B\)- array, these yield inequalities in terms of the \(\mu_ i\)'s and \(m\) when no value for \(l\) is available. These inequalities are stronger than similar known inequalities in certain instances. The author indicates that analogous inequalities can be obtained for \(B\)-arrays of strength \(t\) with \(t\) arbitrary.