Does a larger neural network mean greater information transmission efficiency?

Realistic modeling of brain involves large number of neurons. The important question is how this size affects transmission efficiency? Here, these issue is studied in terms of Shannon's Theory. Mutual Information between input and output signals for simple class of networks with an increasing number of neurons is analyzed theoretically and numerically. Levy-Baxter neural model is applied. It turned out, that for these networks the Mutual Information converges, with increasing size, asymptotically very slowly to saturation level. This suggests that from certain level, the increase of neurons number does not imply significant increase in transmission efficiency, contributes rather to reliability.