In ArcGIS, this can be done with Create random point if you have spatial analyst or 3D analyst or Advanced(ArcInfo) licence
select each shapefile as "constraining_feature_class" and set the "minimum_allowed_distance"to 250 m.
In QGIS, from what I know, you can use "Vector ‣ Research Tools ‣ Random points" with a constraining feature class, but not for distance. Again, you can use this tool in a loop to add points one by one until you reach the required number.
On the other hand, a solution for simple random sampling with distance contraint is to recursively add your random point and erase the buffer around your random point from the feature class until all your features are completely erased. As mentioned by @Whuber, this will not optimize the number of sample points, but you can control the number of points per strata.
Finally, the optimal number of points with a distance constraint can be achieved by systematic sampling : create a grid (with fishnet) with evenly spaced points (in your case 250 m) and randomly select a rotation angle and shift value betwen 0 and 250 in X and Y direction. This will optimize the number of point samples (and you could randomly subselect some points to reach a given number inside each startum). However, note that systematic sample could be biased because of the spatial autocorrelation.
As comments could be deleted at a point, here the answer that helped solve the problem:
Sounds like your polygon data and the points have different CRS.
- Check if your polygon file has a CRS at all
- If 1. is true, check if your QGIS project set to the same CRS
Best Answer
Personally I do not like the random point algorithm in ArcGIS. Alternatively, use Geospatial Modelling Environment's (GME)
genrandompntsfunction. You will be able to identify specific polygons where random points will be excluded (see highlighted area in attached .jpg). Best of all this software is free.