A note on discrete factorial designs of resolution five and seven and balanced arrays (Q2927769)

``A \(B\)-array \(T\) with \(m\) factors (constraints, rows), \(N\) treatment-combinations (runs, columns), two levels (say, \(0\) and \(1\)), and of strength \(t\) \((1 \leq t \leq m\)) is an \((m\times N)\)-matrix \(T\) with elements \(0\) and \(1\) satisfying the following condition: in every \((t \times m)\)-submatrix \(T^*\) of \(T\), each \((t\times 1)\)-vector \(\underline{\alpha}\) of weight \(i\) ( \(0\leq i \leq t\); the weight of \(\underline{\alpha}\) refers to the number of 1s in it) occurs with the same frequency \(\mu_i\) (say). The vector \(\underline{\mu^{\prime} }=(\mu_0,\mu_1,\dots,\mu_{t})\) and \(m\) are called the parmeters of the array \(T\).''NEWLINENEWLINENEWLINEIn this paper, the authors list 3 results without proof for \(B\)-arrays and state, again without proof, 2 theorems which provide inequalities for the cases of \(t=4,6\). They also provide some examples for the cases of \(t=4\) and \(t=6\).NEWLINENEWLINENEWLINEAlthough discrete fractional factorial designs are mentioned in the abstract of the paper, there is no mention of them in the paper.