Latinized Rectangular Lattices

Abstract

RECTANGULAR Lattices, Triple Rectangular Lattices and Near Balance Rectangular Lattices were introduced by Harshbarger (1947, 1949, 1951). Other recent studies on the Rectangular Lattice designs are included among the references. These designs treat specifically the cases where the number of varieties or treatments are the product of two consecutive integers, k(k 1), but they can be extended to other cases where the integers are not consecutive. The Near Balance Rectangular Lattice Designs extend the Rectangular Lattice Designs to the case of k replications. This extension causes the resulting formulas for those of the Near Balance Rectangular Designs to be of less complexity and at the same time more efficient than the earlier designs. It includes as with the earlier designs the recovery of interblock information. The time for calculations in the latest design is much reduced. To construct the Near Balance Rectangular Lattice designs start with a set of k 1 mutually orthogonal k X k Latin squares, in which the first column is in the standard order, e.g. for k = 4