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Robust steganography is a technique of hiding secret messages in images so that the message can be recovered after additional image processing. One of the most popular processing operations is JPEG recompression. Unfortunately, most of today's steganographic methods addressing this issue only provide a probabilistic guarantee of recovering the secret and are consequently not errorless. That is unacceptable since even a single unexpected change can make the whole message unreadable if it is encrypted. We propose to create a robust set of DCT coefficients by inspecting their behavior during recompression, which requires access to the targeted JPEG compressor. This is done by dividing the DCT coefficients into 64 non-overlapping lattices because one embedding change can potentially affect many other coefficients from the same DCT block during recompression. The robustness is then combined with standard steganographic costs creating a lattice embedding scheme robust against JPEG recompression. Through experiments, we show that the size of the robust set and the scheme's security depends on the ordering of lattices during embedding. We verify the validity of the proposed method with three typical JPEG compressors and the {\it Slack} instant messaging application. We benchmark its security for various embedding payloads, three different ways of ordering the lattices, and a range of Quality Factors. Finally, this method is errorless by construction, meaning the embedded message will always be readable.