Example 1-41 Seven scientific workers are engaged in a confidential technical research. Their laboratory is equipped with an "electronic lock", and each person involved in the project has a key to open the "electronic lock". For safety reasons, at least 4 people must be present to open the door of the laboratory. How many features must the "electronic lock" have? How many of these features should each scientific worker's "key" possess?

This is a quantitative study, not a specific design of such a "lock" and "key". To make it easier to understand, you can consider this problem as how many locks should be hung on the door? And how many keys should each scientific worker carry?
To ensure that among 7 people, any 3 people present cannot open at least one lock on the door, according to the one-to-one correspondence principle, the door should have at least $\binom{7}{3}=35$ locks, meaning that the "electronic lock" should have at least 35 features.

For any scientific worker, if 3 out of the remaining 6 people are present, at least one lock should require his presence to be opened. According to the one-to-one correspondence principle, each person should carry at least
$$
\binom{6}{3}=20
$$
keys. In other words, each person's keys should have at least 20 features.