Largest simplex in convex hull of points in n dimensions

Question

Given a convex hull C of a set of points in n dimensions, is there a known algorithm (apart from checking all possibilities) that finds the n+1 corner points of a simplex with the largest volume that is completely in C?

(See this question for the same question about polygons/triangles.)

Answer 1

Doubtful, since the problem has a fixed parameter intractability result:
https://doi.org/10.1016/j.ipl.2006.05.006