Whatever the medium, a batch record must show that the batch was made according to the approved master instructions, by trained people, with the right materials and equipment, and that every critical step and check was done and recorded at the time.
In the US, 21 CFR 211.186 requires master production and control records, and 21 CFR 211.188 requires a batch production and control record for each batch, including the materials used, weights and measures, in-process results, the identity of the people performing and checking each significant step, yield calculations and any investigations. EU GMP Chapter 4, WHO GMP and Revised Schedule M set equivalent expectations.
Paper can meet all of this. The question is how much effort it takes — and how many errors slip through to the review stage.