It's not clear from your statement what you're actually comparing.
You describe f4 at 4 seconds gives you "correct blacks", but you say f8 at 16 seconds gives you a "much darker print". Those aren't really the same thing.
For example, it's normal to do a test to determine the minimum exposure to achieve maximum black in the print (at base+fog in the negative).. That exposure level, however, may result in a very dark print if the negative was underexposed and./or underdeveloped.
I agree with this. I’m inclined to suspect that you have misunderstood the advised procedure. Could you explain in full detail what the advice was, and what you actually did?
Ok so what I have done is this;
First I set the the lens at f/4, timer at 16s, focused the lens, gave the exposure on a scrap paper with Stouffer 21 step Wedge tablet, then I have lowered it to f/4 at 8s and finally to f/4 at 4s, because each time, I thought I could give shorted exposure. Results are below. Arrows are the steps I cannot see the difference with the following black part.
Then I thought, ok because f/4 at 4 seconds should be equal amount of light exposure to the papers with f/8 at 16 seconds (2 stop closing aperture, 2 stops giving more light), I should print my contact sheet at f/8 at 16 seconds. Result below. As you can see it is very dark, not something I have expected based on the above test. Because even at f/4 @16 seconds the image on the top right have some whites.
At this point I thought something is wrong so I have printed at f/4 and 4 seconds. Result below. Now that seems more correct. The images on the top are overexposed but the images on the below should be correct prints at Grade 2 (paper is Fomavariant 312, filter setting is 5M)
Now I have confused and thought, ok f/8 @16s gives a very dark image, how about f/8 @8 seconds. Then I thought still it is too dark, so I have closed the aperture 1 more stop to f/11 and printed with 8 seconds. Now the result is more or less the same to f/4 at 4 seconds.
Please correct me at any stage.
PS we are not discussing my photography skills, and because I have forgotten to put the glass on the negatives, they are blurred, I have corrected that.
Many thanks,
Fatih