Double Youden rectangles of sizes px(2p+1) and (p+1)x(2p+1)

A k x v double Youden rectangle (DYR) is a type of balanced Graeco-Latin design where each Roman letter occurs exactly once in each of the Ic rows, where each Greek letter occurs exactly once in each of the v columns, and where each Roman letter is paired exactly once with each Creek Better. The other properties of a DYR are of balance, and indeed the structure of a DYR incorporates that of a symmetric balanced incomplete block design (SBIBD). Few general methods of construction of DYRs are known, and these cover only some of the sizes k x v with k = p (odd) or p + 1, and v = 2p + 1. Computer searches have however produced DYRs for those such sizes, p less than or equal to 11, for which the existence of a DYR was previously in doubt. The new DYRs have cyclic structures. A consolidated table of DYRs of sizes p x (2p + 1) and (p + 1) x (2p + 1) is provided for p less than or equal to 11; for each of several of the sies, DYRs are given for different inherent SBIBDs.