Point clouds are a widely used format for representing 3D objects and scenes. With the aim of enhancing the streamlined transfer and storage of such data, extensive attention has been directed towards point cloud compression (PCC). This has led to a significant research emphasis on advancing PCC methods. Audio Video coding Standard workgroup (AVS) of China have launched a PCC project, which employs the octree representation to compress the geometry information of point cloud data. This paper aims to improve the coding efficiency of AVS PCC. Specifically, the neighbouring occupancy information is used in various ways to construct efficient context driving geometry entropy coding. To reduce the memory footprint in context construction, a context reduction mechanism is proposed utilizing the historical coding information. Moreover, an adaptive context switching method is proposed to fit the diversity of point cloud distribution. Experimental results show that the proposed octree coding method achieves coding gains over 3.0% and 8.0% for lossless and lossy coding conditions, respectively without runtime increase. Due to the superiority of the proposed method, it has been recently adopted as the geometry coding method in AVS PCC.