Some investigations on orthogonal arrays (Q2721333)

The authors use the third, fourth and sixth moments to derive inequalities for binary orthogonal arrays of strength \(6\) and related balanced arrays. In fact, the bounds obtained are not really bounds on orthogonal arrays \(\text{OA}_{\mu}(6,m,2)\) (\(m\) rows, \(64\mu\) columns, each binary \(6\)-tuple of entries precisely \(\mu\) times in each \(6\)-tuple of rows), but only on those of a special form, containing a complementary pair of columns. The bounds obtained seem to follow from the linear programming bound. This is definitively true for the cases \(m\leq 14,\) which are implied by the Friedman bound (the dual Plotkin bound in the binary case) and the quadratic bound. In fact, the authors compare their results only to the Rao bounds. This is not satisfactory as there are many other bounds. There is no indication that the paper contains any new results at all.