<p>Gaussian random number generators attract great interest due to their applications in various fields. Among other requirements, an efficient hardware implementation, tail precision and a flat spectrum are required for competitive generators. A popular approach in the literature is constructed with maximal sequences, which can be generated via Linear Feedback Shift Registers (LFSRs). An improvement is to use pseudonoise binary sequences and combine them to construct Gaussian random number generators with optimized hardware implementation. Unfortunately, the theoretical basis of these generators has been overlooked in the literature. In this work we rigorously investigate the influence of the parameters of these sequences on the construction. Our findings indicate that a small increase in the number of connections in the LFSR can improve the statistical properties of the generator. Other pseudorandom binary families are compared in terms of efficiency of implementation, and the hardness of the parameter search based on the guarantees given by the Central Limit Theorem (CLT) to assess the quality of the generated samples. Finally, we provide initial computational experiments that support the obtained theoretical results and allow us to discard inadequate parameters for the constructions.</p>