Abstract
Factorial designs with two-level factors represent the smallest factorial experiments. The system of notation and confounding and fractional factorial schemes developed for the $2^N$system are found in standard textbooks of experimental designs. Just as in the $2^N$ system, the general confounding and fractional factorial schemes are possible in $3^N,5^N$, .... , and $\rho^N$ where $\rho$ is a prime number. Hence, we have the $\rho^N$ system. In this article, the author proposes a new algorithm for constructing fractional factorial plans in the $\rho^N$ system.