Strong Bell violations in N level systems

We study the variety of ways in which nonlocality can be experimentally detected in N level systems, with conventional Bell inequality violation. By simple constructions, show that there are an exponentially large number of correlations that violate the inequality strongly, which remain robust at any N. We further formulate the concept of weak classical limit to get a better insight to the so called classical behaviour that quantum systems are expected to exhibit when N->infinity.