I can't say I know everything about concrete but when I build my retainer walls, I use strictly portland cement and sand. When I order it I order a 9-10 sack mix and this concrete, after 7 days of curing, is extremely strong! I couldn't tell you what the exact ratio is from the concrete companies since they keep that a well kept secrete for some darn reason. All I can say is possibly using a 1:1 ratio of clean sand and portland, you should be close. This is what I use when I have to mix my own mix. (This home made mix has not been core tested)
There was a guy that took a core sample of the same type of mix from a redi-mixed company (not from my walls) and it cored out at around 10,000 PSI from what I hear. I was not there personally nor did I see the core sample sheet but that's what I was told.
Using an 18lb sledge hammer is whole lot of work when trying to break 4" of concrete that has been undermined using this mix. Its not lightweight by any means and is very strong.
I hope this helps you get pointed in the right direction if not answering you question exactly.
The main trick when wanting very strong concrete is to mix it VERY DRY!
Here is a video that I helped with from StoneMakers Artisans. A couple parts in this video you can see how try the mix is. In fact, it was slightly to wet for what we do, but this is roughly how dry you want your mix. In fact dryer would be better.
I have heard mixed comments about fibers in concrete, whether or not that actually help the strength of concrete. I would not add fibers to a ball of concrete.
What would the diameter of these balls be?