Norm bound when finding an integer relation via FindIntegerNullVector

Questions
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1

When using FindIntegerNullVector in WolframAlpha online to get an integer relation a=(a_1,\ldots,a_n) between numbers x_i,
an optional parameter d can be given in order to get a vector a of norm not greater than d, if it exists.

I’m not sure if I understand correctly how this works, something odd is happening: for some numbers x_i with n=4 I get the solution a=(1,1,1,-1), which has norm \|a\|=\sqrt{4}=2 (the norm is the 2-norm). Now I search with d<2, but I keep getting the same solution of norm 2 for some values of d (e.g. \sqrt{3}, 5/3, 1.68). You can see it for example in

Am I doing something wrong, or is this a bug?

2

None of the above, really. Mathematica gives a warning message with that result. W|A appears to be suppressing it. Might be a smallish bug, depending on one’s view of such things.

To see the message, try the computation using the Wolfram Cloud:

https://www.wolframcloud.com/

3

Thank you for your answer. Can you please copy the warning message here? I have no access to Mathematica.