We all know the standard base-$2$ representation of integers and many of you will know of Gray codes. Does anybody know of a name (or something I can use to find a good reference) for a method of sequencing a binary representation so that numbers higher in the sequence have more bits set? For example,
$$000, 001, 010, 100, 011, 101, 110, 111.$$
We set $i$ bits until all $n \choose i$ combinations are used, then increment $i$. Does this sequence have a name?