Many programs, few characters
Pyth, Score of 1.664 * 10^26

Since you only have L different chars to choose from, you can maximal generate O(L!) different programs. 

So lets build something really close: By indexing permutations of the alphabet:

I use a following list of characters is:

abcdefghijklmnoppqrstuvwxxyzG."


With these characters I can generate 26!-1 different programs like this:

Program 1: x.pG"abcdefghijklmnopqrstuvwxzy
Program 2: x.pG"abcdefghijklmnopqrstuvwyxz
Program 3: x.pG"abcdefghijklmnopqrstuvwyzx
  ...
Program 403291461126605635583999999: x.pG"zyxwvutsrqponmlkjihgfedcba


Notice I didn't use "abcdefghijklmnopqrstuvwxyz" (sorted alphabet), since I give an index of 0. 

So we got N = 403291461126605635583999999, S = 15, L = 31, which gives a score of 1.663767345141228e+26. 

Explanation:

x.pG"...     
   G       G is pre-initialized with "abc...xyz"
 .p        gives all possible permutations
x   "...   the index of "..." in the permutation list


Notice, that none of the programs will actually run. Because of memory and time. 

edit:

You can even get way higher. For instance by using also the uppercase letters. Gives me a score of about 10^76. 

edit 2: a runnable version

Since none of the programs above is actually runnable, here's one that works. 

x.pSK""Kabcde


The programs are:

Program 1: x.pSK"abced"K
Program 2: x.pSK"abdce"K
Program 3: x.pSK"abdec"K
  ...
Program 117: x.pSK"edbca"K
Program 118: x.pSK"edcab"K
Program 119: x.pSK"edcba"K


Here's an online Demonstration. 

Explanation:

x.pSK"abced"K
    K"abced"   K = "abced"
   S           sort it
 .p            generate all permutations of sorted(K)
x           K  index of K in the permutations. 


N = 119, S = 13, L = 13 gives a score of 0. But If we simply use a dummy char to the list we get N = 119, S = 13, L = 14 and a score of 25.92

Of course we can use more chars than abcde for the permutation. If we use n different chars, we get N = n!-1, S = 15, L = n+8, which gives a score of ~n!/(n-7)!. So we can get pretty much an unlimited score.