Bounds on code distance and efficient fractional factorial experiments

The results presented in this paper are based on the correspondence between error-correcting codes and fractional factorial experiments. It is shown that under certain conditions, one can attain a smaller fractional factorial experiment by increasing the number of levels associated with each factor. The Gilbert-Varshamov and the Singleton bounds are used to obtain bounds on the size of the fractional experiment. Analytical approximations and numerical results are presented.