Heuristics, methods to speed up searches over subsets of big set (combinatorially NP hard probably)
This is not ML but your setup reminds me of the Covering Array Problem, which is used for Software Testing.
If you consider your configuration arrays [0 0 1 0 1 0 1 0 1 .... ] as certain tests run , a typical question is what is the minimum number of tests I need to run while I can cover most different setups? Important to increase test completeness but also minimize time it takes to run them.
Possible some covering array solutions might help. There are even tables that are pre-computed that you can use for different number of N and coverage strengths https://math.nist.gov/coveringarrays/coveringarray.html
And as you pointed out this is a combinatorial problem that suffers from combinatorial explosion. You might want to divide/conquer (split the N into k manageable groups).