A Geometric Construction of Generalized Youden Designs for $\nu$ A Power of a Prime

Abstract

A new method of construction of generalized Youden designs for $\nu = s^m, s$ a power of a prime is introduced here. This generalizes the construction of Ruiz and Seiden which could be applied only to even powers of a prime. The number of experimental units required to carry out the design in the corresponding cases is the same. However, the present method can be used for construction of designs which could not be constructed previously even in the case of even powers. Moreover the present method presents a unified construction for even and odd powers of primes. For a fixed value of a prime it is noticed here that one can construct an infinite number of designs. This provides the experimenter with a choice of designs which may prove very useful in applications. A simpler method of construction is also presented. The price one has to pay for the simplicity is that more experimental units are required for carrying out the design.