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Yea, I believe your right. The reason I was looking for it is since I was looking at some kind of choosing from a worst case subset of the cube vertices that will allow receiving each of the vertices as an affine combination. Thank you!
Great answer, thanks a lot! I do wonder if the true C is n, maybe there's some pathological matrix showing it, but the difference between n^n and c^n is less important to me.
When I said 0-1 I meant values that are only 0 or 1 (binary matrix, but not over Z2). I know that in this case there's a nice bound for the determinant for example. The upper bound is what interests me more.