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Well, EPSG:4326 and EPSG:3857 are common for web mapping and similar (for their difference: (gis.stackexchange.com/questions/34276/…) ). EPSG:21781 is based on a different ellipsoid, so the transformation is not that easy. But you could use the Proj4.js (proj4js.org) library if you are looking for the reprojection parameters.
Please give more context to your questions. I saw your tag for openlayer-3: is your final goal to show the image in openlayer in EPSG:21781? Are your trying to reproject before publishing your images in a webmap? Or do you want to reproject on the fly in the webmap?
