What is the strength and attack vectors of this simple scheme? Let's say that Alice wants to communicate some secret value $S$ to Bob through a public channel in a way that other people don't know what the value was.

To do this, Alice publishes that secret value to the public channel, along with $N-1$ other values, making a list $L$ which has $N$ items in it.

Before this communication, Alice and Bob agreed that the value Alice wanted to communicate to Bob would be $L_M$ where $M \in [0,N)$.

How secure is this scheme?  What attack vectors could be used on it? Also, does this technique have a name?

Some thoughts of my own:


The security of the scheme seems to relate to the size of $N$.  Larger $N$ values seem more secure.
It seems like if you didn't choose the other values of the list carefully, that it could be seen statistically that "one data point doesn't fit with the others" which could make the actual value cared about stick out more obviously.
One idea to make the value fit in completely could be that if the secret value $S$ could be represented in $B$ bits, that maybe the list $L$ could be a random shuffle of all values $[0,2^B)$, but if someone knew that, they could know that the number was probably on the higher side of the values so this may be too naive.
Agreeing on $M$ in advance has the usual key generation / key sharing / key storing problems and attack vectors.  I'm not interested in that part of the problem.
Short answer: Sorry, no, unfortunately your concept is neither a secure, practical nor efficient crypto scheme.

Slightly longer answer: To illustrate the impractically of your scheme, let's assume you are sending a completely random bit string $S$ of length $B$. In such case, in order to preserve perfect secrecy, you will at least have to send a list $L$ containing all possible values $[0..2^B)$ in random order, except for $S$ which is fixed at position $M$, where $M$ is the secret key you share with the recipient. 

Now, if $M$ is selected completely at random from all possible values, it will also be a random element from $[0..2^B)$ and consequently be exactly as long, and contain as much entropy as, the message $S$ you want to sent. 

The cipher text $L$ on the other hand, will be exponentially longer than the plain text message $S$. This is bad, because it means that your effort of sending the message securely, will be exactly as great as the effort you want your adversary to suffer trying to brute force guessing the key or the plain text.

Furthermore, if the plain text $S$ is not completely random, securely executing your scheme gets more complicated, but the conclusion doesn't change. If you maximize security, your effort of encoding and sending the plain text will be no less than the effort you want your adversary to suffer trying to break your scheme.