In ArcGIS, is it possible to create a raster with an associated attribute table where each pixel is represented by a "row" in that table. I would like to specify unique attributes for each raster pixel, rather than for each "Value" of pixels (the default raster attribute table in ArcGIS seems to be one row per "Value" attribute of pixels).
Storing data in a raster has to be done in a "one band <--> one information" logic, and this is valid for any software (not only ArcGIS). Raster "attribute tables"(when they are supported) need to be understood as "look up table", in other words they are tables providing additionnal information about the unique value that is stored in the pixel (full class name, RGB values for the color of the class...). The number of columns in a raster attribute table is not limited, but if you want to store different thematic attributes, you need to create a raster with multiple bands (one band per thematic information). A user clicking on this multi-band image would see all attributes. Note that this set of bands would probably have a good compression ratio and should be stored in band interleave per pixel for fast access to the series of values.
The alternatives are
1) the conversion into point data (vector)
2) the creation of a single complex attribute value (which could have its look up table). If you stack your booleans like this (1001101011010011...101), it creates a binary number which can store any combination. Note that this number will be potentially very large (> 10^15 in your case) and you will need a 64bit integer to store it. However, all combinations are not possible: you will never have more entries than the total number of pixels in your map.