Yeah, of course. I wasn't speaking of the Atari or any computer in any practical sense, just hypothetically about the minimum storage.
Of course it's possible to go even more than that - enumerate every reachable position (so remove situations like a pawn on the first or eighth rank, kings adjacent or in some check situation that couldn't have happened, pawns in positions that would require more captures than there are enemy pieces missing from the board, etc) and assign them all an index number, which requires log N storage size. And of course it would be practically impossible to do anything computationally with positions stored like that.
This link estimates an upper bound of around 10^46 reachable positions, so log2 of that would be only about 150 bits to enumerate them all.
Of course it's possible to go even more than that - enumerate every reachable position (so remove situations like a pawn on the first or eighth rank, kings adjacent or in some check situation that couldn't have happened, pawns in positions that would require more captures than there are enemy pieces missing from the board, etc) and assign them all an index number, which requires log N storage size. And of course it would be practically impossible to do anything computationally with positions stored like that.
This link estimates an upper bound of around 10^46 reachable positions, so log2 of that would be only about 150 bits to enumerate them all.
https://math.stackexchange.com/questions/1406919/how-many-le...