  Some recent work on confidence intervals for randomized quasi-Monte Carlo
(RQMC) sampling found a surprising result: ordinary Student $t$ 95\% confidence
intervals based on a modest number of replicates were seen to be very effective
and even more reliable than some bootstrap $t$ intervals that were expected to
be best. One potential explanation is that those RQMC estimates have small
skewness. In this paper we give conditions under which the skewness is
$O(n^\epsilon)$ for any $\epsilon>0$, so `almost $O(1)$'. Under a random
generator matrix model, we can improve this rate to $O(n^{-1/2+\epsilon})$ with
very high probability. We also improve some probabilistic bounds on the
distribution of the quality parameter $t$ for a digital net in a prime base
under random sampling of generator matrices.
