  This paper presents measurements of the production of Ds- mesons relative to
Ds+ mesons as functions of x_F and square of p_t for a sample of 2445 Ds decays
to phi pi. The Ds mesons were produced in Fermilab experiment E791 with 500
GeV/c pi- mesons incident on one platinum and four carbon foil targets. The
acceptance-corrected integrated asymmetry in the x_F range -0.1 to 0.5 for Ds+-
mesons is 0.032 +- 0.022 +- 0.022, consistent with no net asymmetry. The
results, as functions of x_F and square of p_t, are compared to predictions and
to the large production asymmetry observed for D+- mesons in the same
experiment. These comparisons support the hypothesis that production
asymmetries come from the fragmentation process and not from the charm quark
production itself.
