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Tracking studies including the effects of random multipoles resulting from construction errors have been made for RHIC with two independent tracking programs at three different tunes. The studies were made using ten different sets of random errors for each of the programs. The aperture was defined as the worst case, and the results of the two programs are in good agreement. A second set of studies was made for which the number of dipoles was doubled to determine whether doubling the number of independent random errors results in a reduction of the effects or random multipoles. The results for the two cases, one dipole per half cell and two dipoles per half cell, indicate there is little difference in dynamic aperture.