PUMS data accuracy

Hi, I posting here because I have trouble understanding the text above. The text -page 5- is part of the PUMS -Public Use Microdata Sample-: https://www2.census.gov/programs-surveys/acs/tech_docs/pums/accuracy/2016AccuracyPUMS.pdf

2. Systematic sampling was applied to ACS HUs:

a. Within each state, a random number is chosen between zero and the sampling interval. A counter is initialized with the random number.

b. At each HU record, the value of the counter is incremented by one and compared to the sampling interval.

i. If the counter’s new value is greater than the sampling interval, the HU record is selected for the PUMS and a flag is set to 1. The counter is decreased by the sampling interval with the new value passed to the next record.

ii. If the counter is less than the sampling interval, the HU record is not selected for the PUMS and the value of the counter is passed to the next record without altering its value.

3. All HUs selected for PUMS were placed in the PUMS HU sample file

I would like to say that english its not my native languaje so I might not understand because of that. Having said that, systematic samplig is K=n/N, in this case if belive the Census Bureau its not using that method, instead they are only selecting a random number, and from that number they are picking record to make the sample, ej, if the random number is 3, every 3 record will be selected, 3, 6, 9, 12....

Then, it says that at each record the value if incremented by one and comprared to the sampling interval, I dont fully understand this part, so are they first selecting 3, then 3+1=4, 4+1=5 and so on?

And, if the counter´s new value is greater than the sampling interval how is that record selected? If my sampling interval is 384, and the counter´s new value is 385, how can I select record 385 if such record doest not exists cuz my interval consist of only 384 records?

As you can see, I need help understanding I would truly appreciate if you help me and give me a practical example.

For your time and interested, Ty.
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