New spectrum sharing techniques for assuring the EMC of wireless systems have recently been investigated that enable the joint utilization of all orthogonal electromagnetic (EM) transmission resources, including, but not limited to time, frequency, geographic space, modulation/code, and polarization. This multi-dimensional environment is referred to as the transmission hyperspace (TH), a term intended to convey the notion of a multi-dimensional resource space in which each dimension allows orthogonality amongst users. The challenges faced in the modeling and analyses of large-scale TH-enabled problems are presented in terms of assigning an n-tuple for the purpose of enhancing data throughput amongst a group of intended transceivers. The key aspects of the TH for EMC and efficient spectrum management are discussed. The TH approach is anticipated to provide several orders of magnitude improvement in RF resource utilization and aggregate data throughput