Scalability and performance are major challenges in developing high-performance multicast packet switching technologies in the 5G/6G core networks. We propose a novel scheme called Two-Dimensional Scalar-matrix and Vectors Routing and Forwarding (2D-SVRF) to address these two issues. Our scheme improves upon commonly used algorithms, Bloom filter (BF) and Scalar-pair Vectors Routing and Forwarding (SVRF), which have limitations in space and time efficiency, especially in carrier-grade Packet Forwarding Engines (PFEs) with high port-density and large membership-capacity. 2D-SVRF transforms a scalar-vector into a scalar-matrix by dividing an n-element group into N-rows (sub-blocks) and dividing an output-port bitmap with ρ-elements into M-columns within each sub-block. This enables the reuse of smaller and identical prime keys among different sub-blocks and sub-scalars. By leveraging this approach, multicast forwarding can be partitioned to exploit parallelism, resulting in reduced memory usage and lower computational complexity. Simulation evaluation confirms that 2D-SVRF outperforms competing algorithms in terms of scalability and efficiency, particularly when optimized with the (M, N) parameters. The 2D-SVRF approach is expected to make the implementation of SVRF feasible in carrier-grade multicast-enabled switches and routers.