An algorithm that works for any even n is to generate the Gray code for the next highest power of 2 (in this case, 16) then pick the middle n symbols. Eg the 1

An algorithm that works for any even n is to generate the Gray code for the next highest power of 2 (in this case, 16) then pick the middle n symbols. Eg the 16 position Gray code, with the middle 12 symbols marked: 0000 0001 0011 < 0010 < 0110 < 0111 < 0101 < 0100 < 1100 < 1101 < 1111 < 1110 < 1010 < 1011 < 1001 1000