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There is a result related to the average number of the $(\delta, \eta)$-LLLbases in dimension $n$ in theoretical sense but the formula seems to becomplicated and computing in high dimension takes a long time. In practicalsense, we suggest some approximations which can be computed by just storingsome constants and computing relatively simple exponential functions.

A study on some approximations on the average number of the LLL bases in higher dimensions