Limit of the minimum order of existentially closed graphs

Determine whether the limit lim_{n\to\infty}m_{ec}(n)/(n2^n) exists, where m_{ec}(n) is the minimum order of an n-existentially closed graph.

Background

The paper recalls that Caccetta, Erdős, and Vijayan established the lower bound m_{ec}(n)=\Omega(n2^n) and that the best known general upper bound is O(n^22^n). They conjectured that the normalized quantity m_{ec}(n)/(n2^n) converges as n tends to infinity, but the paper does not resolve this asymptotic question.