Building DNA strands at a high rate that are suitable for data storage. Methods include using DNAzyme and utilizing libraries of pre-prepared oligos. A system for the DNA strand synthesis includes: a DNA symbol library comprising a number of single strand oligo symbols; a DNA linker library comprising a first set of single strand oligo linkers and a second set of single strand oligo linkers; and a DNAzyme library comprising a number of DNAzymes. An S1 end of a first DNAzyme is adapted to join the S1 end of a symbol and an S2 end of the first DNAzyme is adapted to join an S2 end of a first linker, and an S1 end of a second DNAzyme is adapted to join an S1 end of a second linker and an S2 end of the second DNAzyme is adapted to join an S2 end of the symbol.