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# Selection of the notary set size
As mention in our consensus algorithm, we follow the hypergeometric distribution to decide the size of notary set.
Given a node set of size N, the ratio R of Byzantine nodes, and the notary set of size n, then, the probability that more than 1/3 of notary set is Byzantine nodes is
<p align="center">
<img src="https://imgur.com/wszheq8.png" width="250">
</p>
We set the probability to be 10^-8; that is, there is less than one fault during 10000 years in expectation (notary set is re-selected every hour).
Assume R=1/5. We can derive the proper size of the notary set according to the equation and the result is shown in the following figure.
For convenience, we give two curves to approximate the data points.
The first one is y = 70.5 ln(x) - 264, which is the purple dash line and the second one is y = 74 ln(x) - 264, which is the green dash line.
The following table is the resilience ratio to the Byzantine given the size of notary set and probability 10^-8.
| node set size | notary set size | resilience | notary set size | resilience |
| -------- | -------- | -------- | --- | --- |
| 200 | 110 | 0.199 | 123 | 0.220 |
| 400 | 159 | 0.197 | 174 | 0.207 |
| 600 | 187 | 0.194 | 203 | 0.202 |
| 800 | 208 | 0.197 | 224 | 0.202 |
| 1000 | 223 | 0.197 | 252 | 0.202 |
| 1500 | 252 | 0.199 | 270 | 0.204 |
| 2000 | 272 | 0.199 | 291 | 0.207 |
| 4000 | 321 | 0.207 | 342 | 0.209 |
DEXON mainnet will use y = 70.5 ln(x) - 264 to decide the size of the notary set under different sizes of the node set.
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