[lifthrasiir]

An efficient method would be groupping 13 items into groups of 3, 3, 3, 3 and 1 item(s) each, and then encoding 5^3 = 125 possibilities into 7 bits. That leaves 4 bits which can be used to encode the last group without any additional coding. This kind of numerical coincidences is widely used in bitwise encoding (e.g. QR code's numeric and alphanumeric modes make use of the fact that 2^10 / 10^3 and 2^11 / 45^2 are both close to 1 while no less than 1).