Technology provided herein relates in part to methods, processes, machines and apparatuses for determining sequences of nucleotides for nucleic acid templates in a nucleic acid sample. The technology provide herein also relates in part to methods, processes, machines and apparatuses for counting nucleic acid templates. Nucleic acid templates of a sample are tagged with nonrandom oligonucleotide adapters that include predetermined non-randomly generated sequences. The use of these nonrandom oligonucleotide adapters provides an efficient method to reduce sequencing errors, and increase the sensitivity of detection of low-frequency single nucleotide alterations.