  In this paper, we develop an approach for the exact determination of the
minimum sample size for the estimation of a Poisson parameter with prescribed
margin of error and confidence level. The exact computation is made possible by
reducing infinite many evaluations of coverage probability to finite many
evaluations. Such reduction is based on our discovery that the minimum of
coverage probability with respect to a Poisson parameter bounded in an interval
is attained at a discrete set of finite many values.
