Trojan square and incomplete Trojan square designs for crop research

Latin square and near-Latin square designs are valuable row-and-column designs for crop research but the practical size range of such designs is severely limited. Semi-Latin square designs extend this range but not all semi-Latin squares are suitable for experimental designs. Trojan square designs are a special class of optimal semi-Latin squares that generalizes the class of Latin square designs. The construction of Trojan squares both for unstructured and for factorial treatment sets is discussed and the utility of Trojan square designs for practical crop research is demonstrated. The corpus of available designs is further extended by a discussion of incomplete Trojan square designs obtained by omitting one main row or one main column from a complete Trojan square design. Some advantages of Trojan square and incomplete Trojan square designs for crop research are discussed and some suggestions for further design research are made.