PostGIS: Perform a Spatial Join only joining the intersecting polygon with the maximu

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I'd like to perform a spatial join using PostGIS. I've got table_A containing 80.000 entries and table_B containing roughly 1.500.000 entries. The entries in table_B have a column "number".

My goal is to only join the entries from table_B with the maximum value which intersect polygons from table_A.

For example: In the following image I'd like to only join "polygon 3" from table_B to the blue polygon of table_A. Polygon 1 and Polygon 2 should not be joined because they have lower numbers.


Thanks in advance!

ps. I could also use ArcMap (Standard license) but it crashes due to the size of the shapefile (~ 1.8GB).



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