memory - calculating subsets of a matrix (L=40X40)

I need to calculate all $k$-possible subsets$(k:1,L)$ of matrix with size $L$. I am using subset function as following,

L = 10;
Do[
   t = L!/(k! (L - k)!);
   tstmat = RandomReal[L, {L, L}];
   config = Subsets[Range[Length@tstmat], {k}];

   Print[{k, t}]
   , 
   {k, 1, L}
];

this is working fine up to $L=24$, but for big sizes I am running into memory issues,

L | mem

25 | 2.152 G

26 | 3.600 G

27 | 6.470 G

28 | 12.418 G

29 | 23.641 G

I am assuming the huge memory is related to part of code where it's calculating the different subsets and keeps all of different configuration, for example for size L=30 and L=40 this becomes on the order of 10^9 and 10^12 sub-lists, respectively. Is there any way to decrease the memory, for example by keeping subsets once at a time? Or maybe is there any other function in Mathematica to calculate the all possible subsets?

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