Several posts in the forum suggest using this lattice estimator to estimate the security level, but how do OpenFHE parameters relate with the ones in the estimator?

n

the dimension of the LWE sample vector (Z/qZ)^n.

q

the modulus of the space Z/qZ of integers the LWE samples are in.

Xs

the distribution on Z/qZ from which the LWE secret is drawn

Xe

the distribution on Z/qZ from which the error term is drawn

I assume n is BatchSize, q is ModSize, and Xs is related to SecretKeyDist? How can I extract the correct parameters from OpenFHE?

It does not seem right. According to Table 1 of https://homomorphicencryption.org/wp-content/uploads/2018/11/HomomorphicEncryptionStandardv1.1.pdf, one can use n=2^{15} up to \log q = 881. Even more refined estimates using the latest lattice estimator (and MATZOV cost model) suggest one can use n=2^{15} up to \log q = 868. So I suspect you are not using the lattice estimator correctly. I am not an expert in the lattice estimator, but I typically specify the uniform ternary distribution not as Xs=estimator.nd.NoiseDistribution.UniformMod(3) but using Xs = ND.Uniform(-1,1,n) instead

I would run the test using the following command (I started it on my machine but it is taking too long - I will add it here if I get a result later).