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Given a lattice $L = \bigoplus_{i=1}^{m} \mathbb{Z}v_i$ (the $v_i$ are linearly independent vectors in $\mathbb{R}^n$) and a number $c > 0$, can one quickly compute or find a good estimate on the number of lattice vectors $v$ with $|v| \leq c$ without actually enumerating these vectors? The basis $v_1,\ldots, v_m$ of the lattice can be assumed to be LLL reduced.

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closed as not constructive by Kaveh Jul 23 '11 at 12:38

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

Simultaneous cross-posting on different sites is discouraged, please wait a few days to see if you get an answer on one site before posting it on another one. I am closing the question for now, wait a few days and if you still don't get a satisfying answer on the other site flag the question and we will reopen this question. – Kaveh Jul 23 '11 at 12:40
Sorry. Thanks for letting me know. – OSHE Jul 23 '11 at 16:36