Compress 21 Alphanumeric Characters in to 16 Bytes

I'm trying to take 21 bytes of data which uniquely identifies a trade and store it in a 16 byte char array. I'm having trouble coming up with the right algorithm for this.

The trade ID which I'm trying to compress consists of 2 fields:

1. 18 alphanumeric characters consisting of the ASCII characters 0x20 to 0x7E, Inclusive. (32-126)
2. A 3-character numeric string "000" to "999"

So a C++ class that would encompass this data looks like this:

class ID
{
public:
    char trade_num_[18];
    char broker_[3];
};

This data needs to be stored in a 16-char data structure, which looks like this:

class Compressed
{
public:
    char sku_[16];    
};

I tried to take advantage of the fact that since the characters in trade_num_ are only 0-127 there was 1 unused bit in each character. Similarly, 999 in binary is 1111100111, which is only 10 bits -- 6 bits short of a 2-byte word. But when I work out how much I can squeeze this down, the smallest I can make it is 17 bytes; one byte too big.

Any ideas?

By the way, trade_num_ is a misnomer. It can contain letters and other characters. That's what the spec says.

EDIT: Sorry for the confusion. The trade_num_ field is indeed 18 bytes and not 16. After I posted this thread my internet connection died and I could not get back to this thread until just now.

EDIT2: I think it is safe to make an assumption about the dataset. For the trade_num_ field, we can assume that the non-printable ASCII characters 0-31 will not be present. Nor will ASCII codes 127 or 126 (~). All the others might be present, including upper and lower case letters, numbers and punctuations. This leaves a total of 94 characters in the set that trade_num_ will be comprised of, ASCII codes 32 through 125, inclusive.