We show that it is not possible to approximate the minimum Steiner tree problem within 1+1162 unless RP=NP. The currently best known lower bound is 1+1400. The reduction is from Håstad's nonapproximability result for maximum satisfiability of linear equation modulo2. The improvement on the nonapproximability ratio is mainly based on the fact that our reduction does not use variable gadgets. This idea was introduced by Papadimitriou and Vempala. © 2002 Elsevier Science B.V. All rights reserved.
Thimm, M. (2003). On the approximability of the Steiner tree problem. In Theoretical Computer Science (Vol. 295, pp. 387–402). https://doi.org/10.1016/S0304-3975(02)00414-0