The generation of synthetic genomic sequences using neural networks has potential to ameliorate privacy and data sharing concerns and to mitigate potential bias within datasets due to under-representation of some population groups. However, there is not a consensus on which architectures, training procedures, and evaluation metrics should be used when simulating single nucleotide polymorphism (SNP) sequences with neural networks. In this paper, we explore the use of Generative Moment Matching Networks (GMMNs) for SNP simulation, we present some architectural and procedural changes to properly train the networks, and we introduce an evaluation scheme to qualitatively and quantitatively assess the quality of the simulated sequences.