A New Family of Nested Row-Column Designs

Using the characterization of those prime powers \(q\) for which \({GF}(q)\) admits a quadratic starter: i.e. a pairing \((x_i, y_i)\), \(i = 1, 2, \ldots, \frac{q-1}{2}\), of nonzero squares \(x_i\) with non-squares \(y_i\) in \({GF}(q)\) such that the differences \(\pm(x_i – y_i)\) are all distinct, we obtain a new infinite family of nested row-column designs.