To beat it you must encode each piece with a different number of bits. E.g.
Q c00
N c01
P c10
B c110
R c1110
K c1111
where c is 0 for white or 1 for black. Since there are 2xK, 2xQ, 4xB, 4xN, 4xR, 16xP, you will need 2x5 + 2x3 + 4x4 + 4x3 + 4x5 + 16x3 = 112 bits. Adding the 64 bits for the bitmap, the grand total would be 176 bits.
The issue is that each time a P is promoted to R or B (a stupid thing to do, since a Q would be better) you need one or two bits more. On the other hand, you spare 3 to 5 bits for each captured piece. In normal play, captures outnumber promotions, and promotions are either to Q or N, never R or B, but theoretically...
To beat it you must encode each piece with a different number of bits. E.g.
where c is 0 for white or 1 for black. Since there are 2xK, 2xQ, 4xB, 4xN, 4xR, 16xP, you will need 2x5 + 2x3 + 4x4 + 4x3 + 4x5 + 16x3 = 112 bits. Adding the 64 bits for the bitmap, the grand total would be 176 bits.The issue is that each time a P is promoted to R or B (a stupid thing to do, since a Q would be better) you need one or two bits more. On the other hand, you spare 3 to 5 bits for each captured piece. In normal play, captures outnumber promotions, and promotions are either to Q or N, never R or B, but theoretically...