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A Freeman-Youden rectangle (FYR) is a Graeco-Latin row-column design consisting of a balanced superimposition of two Youden squares. There are well known infinite series of FYRs of size \(q \times (2q+1)\) and \((q+1) \times (2q+1)\) where \(2q+1\) is a prime power congruent to \(3\) (modulo \(4\)). However, Preece and Cameron [9] additionally gave a single FYR of size \(7 \times 15\). This isolated example is now shown to belong to one of a set of infinite series of FYRs of size \(q \times (2q+1)\) where \(q\), but not necessarily \(2q+1\), is a prime power congruent to \(3\) (modulo \(4\)), \(q > 3\); there are associated series of FYRs of size \((q+1) \times (2q+1)\). Both the old and the new methodologies provide FYRs of sizes \(q \times (2q+1)\) and \((q+1) \times (2q+1)\) where both \(q\) and \(2q+1\) are congruent to \(3\) (modulo \(4\)), \(q > 3\); we give special attention to the smallest such size, namely \(11 \times 23\).