This paper creates a new cylindrical time-frequency network that can provide random multiple access by combining time division multiple access (TDMA) and frequency division multiple access (FDMA), abbreviated as TFDMA. A TFDMA-based transceiver is defined that uses a permutation matrix (PM) to model an n × n modulated matrix signal. The PM is isomorphic to a code word of an (n,n(n-1),n-1) permutation group code (PGC). An n-dimensional high-order multi-domain modulated signal constellation is thus created. The proposed TFDMA technique not only allows the maximum number of users to reach over 6000 in one second but also improves the anti-interference capacity for the existing compatible systems. In the same case of anti-interference capacity, should it become possible to overcome the one millisecond latency barrier, the maximum number of users could exceed 50000 in one second.