My university requires that I take attendance. How should I treat students who arrive late to class?

I might soon teach at a university which requires that I record attendance of students, as follows: Attendance is a requirement for the course. A person with at least 75% of attendance is eligible to take final exams. A person with an attendance between 65% and 75% is required to submit a medical certificate. A person with less than 65% of attendance is not allowed to write the exam and has to do recourse.

As the university has no explicit rules on how attendance should be recorded, I am asking about this.

I studied many courses, and the behaviour of faculty in this particular aspect varies from one another. The following are the behaviours of faculties I observed mostly:

1. 
   

   Allowing the latecomer into the class at any time and giving attendance to the latecomer.

   
   


2. 
   

   Allowing the latecomer into the class at any time, asking a reason for being late, and then giving attendance to the latecomer.

   
   


3. 
   

   Allowing the latecomer into the class, but giving attendance based on the reason the latecomer gives for being late.

   
   


4. 
   
   

   Disallowing the latecomer by closing doors or with strict instruction.

   
   

So, I came to the impression that it totally depends on the particular faculty. Mostly I observed 1, 2 and 4. I observed 3 very rarely.

What is the recommended and proper behaviour towards latecomers?