With the rapid developments in the Internet of Things (IoT), low power wide area networks (LPWAN) framework, which is a low-power, long-distance communication method, is attracting attention. However, in LPWAN, the access time is limited by Duty Cycle (DC) to avoid mutual interference. Packet-level index modulation (PLIM) is a modulation scheme that uses a combination of the transmission time and frequency channel of a packet as an index, enabling throughput expansion even under DC constraints. The indexes used in PLIM are transmitted according to the mapping. However, when many sensors access the same index, packet collisions occur owing to selecting the same index. Therefore, we propose a mapping design for PLIM using mathematical optimization. The mapping was designed and modeled as a quadratic integer programming problem. The results of the computer simulation evaluations were used to realize the design of PLIM, which achieved excellent sensor information aggregation in terms of environmental monitoring accuracy.