A machine-implemented method of constructing multidimensional constellations having increased minimum distances between the constellation symbols thereof compared to those of comparable conventional constellations, e.g., QPSK and QAM constellations. An example multidimensional constellation so constructed may have eight or more dimensions and may be mapped onto degrees of freedom selected from, e.g., time, space, wavelength, polarization, and the in-phase and quadrature-phase components, of the optical field. The disclosed method is beneficially used to generate multidimensional modulation formats characterized by constant total optical transmit power per modulation time slot and/or applicable to the transmission of multidimensional constellation symbols having separate parts thereof primarily carried by different respective guided modes of the optical fiber. Example methods and apparatus for implementing such multidimensional modulation formats are also disclosed herein.