About security level of ciphertexts in HEAAN (or any FHE scheme for that matter)

[imtiyazuddin]

About security level of ciphertexts in HEAAN (or any FHE scheme for that matter)
If we see sagemathcell implementation of tester for checking security levels for given paramters, as we increase logq for same n value, it says security level also increases. is this true??
If so why not just set n to 1024 and increase only logq to meet different application requirements, i.e. higher multiplicative depth??