Generating entanglement in a distributed scenario is a fundamental task for implementing the quantum network of the future. We here report a protocol that uses only linear optics for generating GHZ states with high fidelities in a nearby node configuration. Moreover, we analytically show that the scheme provides the highest success probability, and, then, the highest generation rate for sequential protocols. We furthermore show how to retrieve the same results using a numerical approach. Both the analytical proof and the numerical optimization represent a novelty in the field of entanglement generation in quantum networks and are tools for further investigation. Finally, we give some estimates for the generation rate in a real scenario.