This paper investigates the compositional abstraction-based synthesis of least restrictive, controllable, and nonblocking supervisors for discrete event systems that are given as a large number of finite-state machines. It compares a previous algorithm that synthesises modular supervisors in the form of state machines, with an alternative that records state maps after each abstraction step and uses these to control the system. The state map-based algorithm supports all abstraction methods used previously, and in addition allows for nondeterminism, hiding, and transition removal. It has been implemented in the software tool Supremica and applied to several large industrial models. The experimental results and the complexity analysis show that state maps can be computed efficiently and in many cases require less memory than state machine-based supervisors.