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

Abstract

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

14 pages