Oh, something I forgot to mention: I tried using a constant number of bits but varying the vector size/quantity to see how things scaled. In other words, I compared:

I found more smaller vectors works better until the number of samples matches the number if bits in the smaller vector. Plotting the functions:

(1-exp(-x/1000))^10
(1-exp(-x/2000))^5
(1-exp(-x/2500))^4
(1-exp(-x/3333))^3
1-exp(-x/10000)
[download]

using a graphing calculator shows that's where the curves cross:

...roboticus

When your only tool is a hammer, all problems look like your thumb.