The inductor with the lowest initial permeability core and the greatest number of turns shows the least decline of inductance value for DC currents.
I had a need for an inductor for a switch-mode power supply whose nominal inductance value would be 100µHy. I knew of course that the actual inductance would be lessened as DC load current went up, but I wanted to know by how much and maybe to see what control I might have over that. My available test equipment for the purpose was rather limited, so I had to do things a bit differently.
I had four types of toroidal cores from which to choose, each with a different value of nominal permeability. For each one, I worked out the number of turns of wire that would yield as close to 100µHy as I could get it to be at zero current and then I set out to test each one for its decline of inductance versus DC current as in the following sketch.
Just to mention, the variable DC power supply I used was a brute. It had been made by Lambda, possibly in prehistoric time. It was designed for 19-inch rack mounting and it was so heavy that Charles Atlas might have had second thoughts about lifting it alone. There was some IRON in there. In any case though, I put some bypass capacitors across the power supply's output terminals and trusted to the powers that be that the source impedance of everything would be negligibly low at my test frequency of 100kHz.
I was fortunate to have on hand two identical inductors of rather large size from which I was able to derive the "reference inductance" that I was going to need. By placing one of them in the test set-up as the reference and the other one as the D.U.T., I ran the described test and got a value for the paralleled pair's net inductance. Since the two were equal, each of them was taken to have twice the obtained inductance value for each DC current level I used. I then arbitrarily chose one of them to be the reference for the testing of each of my candidate inductors. I ended up with the following results.
The inductor that had the lowest initial permeability core and the greatest number of turns showed the least decline of inductance value for DC currents from zero to my maximum. The inductor that had the highest initial permeability core and the smallest number of turns of wire showed the greatest decline of inductance value for DC currents from zero to my maximum.
In hindsight, I guess I should have expected this, but it was good to get some hard test results that were specific to my particular application.