A New Family of Nested Row-Column Designs

Abstract

Using the characterization of those prime powers $q$ for which $GF(q)$ admits a quadratic starter: i.e. a pairing $(x_i,y_i)$, $i=1,2,\dots ,\frac{q-1}{2}$, 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.