Non-linear precoding (NLP) scheme for downlink multi-user multiple-input multiple-output (DL-MU-MIMO) transmission has received much attention as a promising technology to achieve high capacity within the limited bandwidths available to radio access systems. In order to minimize the required transmission power for DL-MU-MIMO and achieve high spectrum efficiency, Vector Perturbation (VP) was proposed as an optimal NLP scheme. Unfortunately, the original VP suffers from significant computation complexity in detecting the optimal perturbation vector from an infinite number of the candidates. To reduce the complexity with near transmission performance of VP, several recent studies investigated various efficient NLP schemes based on the concept of Tomlinson-Harashima precoding (THP) that applies successive pre-cancellation of inter-user interference (IUI) and offsets the transmission vector based on a modulo operation. In order to attain transmission performance improvement over the original THP, a previous work proposed Minimum Mean Square Error based THP (MMSE-THP) employing IUI successive pre-cancellation based on MMSE criteria. On the other hand, to improve the transmission performance of MMSE-THP, other previous works proposed Ordered MMSE-THP and Lattice-Reduction-Aided MMSE-THP (LRA MMSE-THP). This paper investigates the further transmission performance improvement of Ordered MMSE-THP and LRA MMSE-THP. This paper starts by proposing an extension of MMSE-THP employing a perturbation vector search (PVS), called PVS MMSE-THP as a novel NLP scheme, where the modulo operation is substituted by PVS and a subtraction operation from the transmit signal vector. Then, it introduces an efficient search algorithm of appropriate perturbation vector based on a depth-first branch-and-bound search for PVS MMSE-THP. Next, it also evaluates the transmission performance of PVS MMSE-THP with the appropriate perturbation vector detected by the efficient search algorithm. Computer simulations quantitatively clarify that PVS MMSE-THP achieves better transmission performance than the conventional NLP schemes. Moreover, it also clarifies that PVS MMSE-THP increases the effect of required transmission power reduction with the number of transmit antennas compared to the conventional NLP schemes.