  In the recent article [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva,
L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that
for every arbitrarily slow convergence speed and every natural number $d \in
\{4,5,\ldots\}$ there exist $d$-dimensional stochastic differential equations
(SDEs) with infinitely often differentiable and globally bounded coefficients
such that no approximation method based on finitely many observations of the
driving Brownian motion can converge in absolute mean to the solution faster
than the given speed of convergence. In this paper we strengthen the above
result by proving that this slow convergence phenomena also arises in two
($d=2$) and three ($d=3$) space dimensions.
