  It's well-known that there is a very powerful error bound for Gaussians put
forward by Madych and Nelson in 1992. It's of the form$% | f(x)-s(x)| \leq
(Cd)^{\frac{c}{d}}\left\Vert f\right\Vert_{h}$ where $C,c$ are constants, $h$
is the Gaussian function, $% s$ is the interpolating function, and d is called
fill distance which, roughly speaking, measures the spacing of the points at
which interpolation occurs. This error bound gets small very fast as $d\to 0$.
The constants $C$ and $c$ are very sensitive. A slight change of them will
result in a huge change of the error bound. The number $c$ can be calculated as
shown in [9]. However, $C$ cannot be calculated, or even approximated. This is
a famous question in the theory of radial basis functions. The purpose of this
paper is to answer this question.
