The \(T_{4}\), and \(G_{4}\) constructions of Costas Arrays

We examine two particular constructions of Costas arrays known as the Taylor variant of the Lempel construction, or the \(T_4\) construction, and the variant of the Golomb construction, or the \(G_4\) construction. We connect these with Fibonacci primitive roots, and show that under the Extended Riemann Hypothesis, the \(T_4\) and \(G_4\) constructions are valid infinitely often.