Is this smaller grid for Poisson disc sampling still correct?
You approach will work, and in general any square of size &lt;  will work fine because the invariant "at most 1 point per square" is valid. Extrapolating from your idea, it means that one should get the best reduction in area checks for infinitesimally small squares. But we don't want to do that, right?

There are two reasons why  is usually better than :


How much state do you want to manage? Each square can either be "occupied" or "unoccupied" and contains a pointer to its sample point (if any).

For very large domains with small r, storage costs can be hard to manage. The problem is much worse if you're working with many dimensions. See Gamito et al.'s paper, Figure 12. Even in 4D you can be severely storage limited.
In your proposed grid size, each candidate points checks 24 squares, as opposed to 20 in the usual method. There is a per-square cost (e.g. checking whether square is occupied and fetching sample point if it is) which increases the overall cost in your method.


Basically, your method works, but it is usually not more efficient. 

However, the state of the art in unbiased Poisson-disk sampling techniques actually successively reduces the grid size as the uncovered area reduces. In addition to Gamito et al.'s paper, also see Ebeida et al.'s paper.

P.S. Sorry, I don't know how to do math formatting in Stack Exchange.