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After decades of development, flow-based microfluidic biochips have become an increasingly attractive platform for biochemical experiments. The fluid transportation and the on-chip device operation are controlled by microvalves, which are driven by external pneumatic controllers. To meet the increasingly complex experimental demands, the number of microvalves has significantly increased, making it necessary to adopt multiplexers (MUXes) for the actuation of microvalves. However, existing MUX designs have limited coding capacities, resulting in area overhead and excessive chip-to-world interface. This paper proposes a novel gate structure for modifying the current MUX architecture, along with a mixed coding strategy that achieves the maximum coding capacity within the modified MUX architecture. Additionally, an efficient synthesis tool for the mixed-coding-based MUXes (LaMUXes) is presented. Experimental results demonstrate that the LaMUX is exceptionally efficient, substantially reducing the usage of pneumatic controllers and microvalves compared to existing MUX designs.