The most important fact has not been checked. Since you're using 1AP per classroom you should survey those areas around that classroom and above and below to see how far that signal actually bleeds even at lowest transmit powers. Keep in mind that although people use -67 dBm as a celborder definition, the signal can cause signal detect at 4 dB above noise floor. That means if your noise floor is -92 at your area your AP and connected clients can still be heard at -88 dBm from neighboring AP's causing deferred transmissions. So when determining your channel plan, see how far the signal goes down to -86 or -88 depending on noise and that is your actual border wherein you cannot reuse that channel. So if you still have room for enough channels, then go with 40MHz, but if you don't have enough channels, move down to 20MHz. Also consider changing your RX-SOP thresholds. And of course use high mandatory datarates like 24Mbps minimum to avoid overhead.
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