  In this article, we show that a linear combination $X$ of $n$ independent,
unbiased Bernoulli random variables $\{X_k\}$ can match the first $2n$ moments
of a random variable $Y$ which is uniform on an interval. More generally, for
each $p \ge 2$, each $X_k$ can be uniform on an arithmetic progression of
length $p$. All values of $X$ lie in the range of $Y$, and their ordering as
real numbers coincides with dictionary order on the vector $(X_1,...,X_n)$.
  The construction involves the roots of truncated $q$-exponential series. It
applies to a construction in numerical cubature using error-correcting codes
[arXiv:math.NA/0402047]. For example, when $n=2$ and $p=2$, the values of $X$
are the 4-point Chebyshev quadrature formula.
