Okay,
By definition, and practice, trusses are going to be efficient structures. So let’s assume that you mean: Which truss configuration meet’s all the design criteria using the least material.
Almost any triangulated truss system that has gone through an optimation process is going to come close. But, you still have a major hurdle that going to mess up your efficiency. Local building or engineering departments.
You want to build your structure for the least amount of money, but you can’t until you’ve been reviewed and approved by your local governing authority. They will add to it until they are satisfied that you aren’t going to damage anything with your design. But I digress.
For the simple beam truss the “eccentrically braced truss” pretty much is the best. This is a typical truss with alternating web legs, but there is a space between the legs rather than them meeting at a point.
For slightly better some of the AI designed dendric (treelike) or fractal web trusses can get a little more out of a material.
For less traditional truss systems try curved hollow tubes with spirally hollow tube stiffening supports. Think bird bones or hollow objects curving in as many independent directions as possible. Folding membranes gets you there as well.
Hopefully that helps.