# Query complexity of ANN based on Hamming distance

Ilya R provides the following query complexity of ANN for Hamming distance based on coordinate sampling

https://www.ilyaraz.org/static/class_2018/files/20181023.pdf

When he says k point locations in #3 (see pic) does it mean the time for computing the hash of the query $$q$$? If yes then why does it say k point locations instead of k coordinates? Because I think the steps are :

1. Using the sampled coordinates (pre-determined) hash the incoming query
2. Scan through each point $$p$$ in the indexed hash bucket
3. Perform an exact comparison to see if $$p$$ is an ANN