  In this article, recent results about point processes are used in sampling
theory. Precisely, we define and study a new class of sampling designs:
determinantal sampling designs. The law of such designs is known, and there
exists a simple selection algorithm. We compute exactly the variance of linear
estimators constructed upon these designs by using the first and second order
inclusion probabilities. Moreover, we obtain asymptotic and finite sample
theorems. We construct explicitly fixed size determinantal sampling designs
with given first order inclusion probabilities. We also address the search of
optimal determinantal sampling designs.
