As an inexpensive, scalable Internet-access wireless network, we have studied the architecture, protocols, and design optimizations of the wireless Internet-access mesh network (WIMNET) that uses multiple access-points (APs) connected by wireless links. WIMNET can improve the dependability to failures of links and/or APs by allocating APs redundantly in the network field. Because redundant APs can increase the operational cost and degrade the performance due to increasing radio interferences, only the necessary APs for connections between the hosts and the Internet gateway should be activated at communications. Previously, we have defined the active AP selection problem of selecting the minimum number of active APs, and proposed its heuristic algorithm, assuming that every link has the same constant speed for simplicity. However, our preliminary experiments found that the link speed is greatly affected by the distance in the high-speed IEEE802.11n protocol that has recently become popular. In this paper, we propose a modification of the active AP selection algorithm to consider the link speed change, where we introduce a new design parameter for WIMNET to select links that have sufficient throughputs. We verify the effectiveness of our modified algorithm through simulations in four instances using the WIMNET simulator.