Network reconstruction of dynamical continuous-time (CT) systems is motivated by applications in many fields. Due to experimental limitations, especially in biology, data can be sampled at low frequencies, leading to significant challenges in network inference. We introduce the concept of "system aliasing" and characterize the minimal sampling frequency that allows reconstruction of CT systems from low sampled data. A test criterion is also proposed to detect the presence of system aliasing. With no system aliasing, this article provides an algorithm to reconstruct dynamic networks from full-state measurements in the presence of noise. With system aliasing, we add additional prior information such as sparsity to overcome the lack of identifiability. This article opens new directions in modeling of network systems where samples have significant costs. Such tools are essential to process available data in applications subject to experimental limitations.