Some tips to help with keeping the eggs cleaner:
Check and clean the butts of your hens and trim some fluff if necessary.
Lay out some roosts and sand around/in front of the nest boxes which helps to clean their feet before entering.
Use wood chips (soft wood shavings) in nest boxes.
Install a poop board to catch the nightly droppings. This will make it easier to inspect for health, to clean out and keeps the floor cleaner.
ETA: Added "soft wood shavings" to clearify, thanks @BDutch
	
		
			
		
		
	
				
			Check and clean the butts of your hens and trim some fluff if necessary.
Lay out some roosts and sand around/in front of the nest boxes which helps to clean their feet before entering.
Use wood chips (soft wood shavings) in nest boxes.
Install a poop board to catch the nightly droppings. This will make it easier to inspect for health, to clean out and keeps the floor cleaner.
ETA: Added "soft wood shavings" to clearify, thanks @BDutch
			
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 I don't know what free resources you have available in Slovakia, but there should be something free you could use instead of buying expensive bedding for the nest boxes. I have successfully used everything from free wood chips, to leaves, to dried grass. Now, I use paper shreds and shredded cardboard which I shred at home for free.
