The 3-partition as defined here is a strongly NP-complete decision problem. Consider one optimization problem of 3-partition where the $m$ subsets each have at most three elements and a sum of not more than $B$ The goal is to minimize $s(S) - \sum_{k=1}^{m} s(S_k)$, i.e. the total value of leftover elements.
This is obviously strongly NP-complete as well. I am asking if anyone is aware of approximation/inapproximability results (other than the obvious nonexistence of FPTAS). I tried searching, but maybe I am not using the correct keywords.
EDIT: As pointed out in the comment below, there is no constant-factor approximation. Are there any (non-constant) approximation results?