This work is focused on the construction of four-dimensional lattices from the algebraic number field Q(√2,√5). Our goal is to construct lattices with a high center densityand a high relative minimum product distance. Achieving good results for those parameters allows the respective signal constellations to perform well over certain communication channels such as the Rayleigh fading and the Gaussian channels. An overview of how lattices can be constructed from submodules of the ring of integers of Q(√2,√5) is presented, as well as a new method that we use for the main results of this work. Our results for the center density were promising: In fact, the value we obtained was 0.124968, which is very close to the upper bound, namely, 0.125 (the original method produced lattices with maximum center density around 0.1118). The results for the relative minimum product distance were an improvement of the previous method, but there is still room for improvement. However, that was left as an object of future study.
