On the Number of \(6 \times 7\) Double Youden Rectangles

Results concerning the enumeration and classification of \(7\times7\) Latin squares are used to enumerate and classify all non-isomorphic Youden squares of order \(6\times7\). We show that the number of non-isomorphic Youden squares obtainable from a species of Latin square Latin Square \({\delta}\), depends on the number of distinct adjugate sets and the order of the automorphism group of Latin Square\({\delta}\). Further, we use the results obtained for \(6\times7\) Youden squares as a basis for the enumeration and classification of \(6\times7\) DYRs.