This document presents two improved biological sequence compression algorithms that utilize a lookup table (LUT) and identification of tandem repeats in sequences. The first algorithm maps all possible 3-character combinations to ASCII characters using a 125-entry LUT. The second maps all possible 4-character combinations to ASCII characters using a 256-entry LUT. These algorithms aim to achieve high compression factors, saving percentages, and faster compression/decompression times compared to previous biological sequence compression methods.