I remember asking myself this question years ago, and came to 162 bits. I was just a kid back then so the logic is probably wrong but I do wonder how simple the encoding could be under those constraints...
Edit: Here are the Notes
0 Empty
10 Pawn
1100 Knight
1101 Rook
1110 Bishop
1111 Queen
32 + 32 + 472
2 times 6 bits: position of the kings
30 bits: color mask
120 + 2*6 + 30 = 162 bits
We can store the rest using the methods from the blog post and add 18 bits for promotion, giving 180 bits.
I'm sure this isn't the most efficient way, and I think I had other methods and considered things like the bishops being able to occupy 32 squares, though special casing doesn't make sense because of promotions.
Technically if you got 8 bishops/queens/knights/rooks
You would occupy another 16 bits, giving 196 bits
I think the upper limit can be reduced at the cost of increasing the lower limit
EDIT2: I think I made the assumption at the time that to promote one piece you needed to capture at least one enemy pawn, giving the space for the two bits, which means the upper bound is actually 180 bits
Would love to see other people try in the comment section
Edit: Here are the Notes
0 Empty
10 Pawn
1100 Knight
1101 Rook
1110 Bishop
1111 Queen
32 + 32 + 472
2 times 6 bits: position of the kings
30 bits: color mask
120 + 2*6 + 30 = 162 bits
We can store the rest using the methods from the blog post and add 18 bits for promotion, giving 180 bits.
I'm sure this isn't the most efficient way, and I think I had other methods and considered things like the bishops being able to occupy 32 squares, though special casing doesn't make sense because of promotions.
Technically if you got 8 bishops/queens/knights/rooks You would occupy another 16 bits, giving 196 bits
I think the upper limit can be reduced at the cost of increasing the lower limit
EDIT2: I think I made the assumption at the time that to promote one piece you needed to capture at least one enemy pawn, giving the space for the two bits, which means the upper bound is actually 180 bits
Would love to see other people try in the comment section