Algebraic constructions of densest lattices

The aim of this paper is to investigate rotated versions of the densest known lattices in dimensions 2, 3, 4, 5, 6, 7, 8, 12 and 24 constructed via ideals and free ZZ-modules that are not ideals in subfields of cyclotomic fields. The focus is on totally real number fields and the associated full diversity lattices which may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. We also discuss on the existence of a number field KK such that it is possible to obtain the lattices A2A2, E6E6 and E7E7 via a twisted embedding applied to a fractional ideal of OKOK.