Wolfram|Alpha's Turing machine enumeration?

Hello, everyone. I’ve been trying to figure it out how does Turing Machines are enumerated in Wolphram Alpha. I’ve tested the first 4096 Turing machines, which are all 2-symbols, 2-states machines. But after that, I don´t understand how the enumeration is done. I also don’t know why all of the 4096 2-symbols, 2-states machines have all their transitions defined [For every state q, and symbol a, d(q, a) exists]. What about the machines whit non-defined transitions? Are those machines out of the enumeration?

Take a look at NKS book, WL docs, and Demonstrations Project: