In 2002, by using Floer theory, Froyshov defined the $h$-invariant for intergal homology 3-spheres, which is a surjective group homomorphism $\Theta^3_{\Bbb Z}\to \Bbb Z$, where $\Theta^3_{\Bbb Z}$ is the group of homology cobordism classes of integral homology 3-spheres with connected sum as operation. (https://arxiv.org/pdf/math/9903083.pdf)

For Seifert homology spheres $\Sigma(a_1,\dots,a_n)$, there are some examples whose $h$-invariants are known. But is there a theorem or algorithm or formula concerning about a way to compute the $h$-invariant for a general Seifert homology sphere $\Sigma(a_1,\dots,a_n)$?

For the Ozsvath-Szabo $d$-invariant, a group homomorphism $\Theta^3_{\Bbb Z}\to 2\Bbb Z$ (which is also defined using Floer theory), there are some ways to calculate it for Seifert homology spheres (e.g. https://arxiv.org/pdf/math/0310083.pdf), but I cannot find any results for computing the $h$-invariant for Seifert homology spheres.