Here's why:

* Complexity: Eukaryotic cells are incredibly complex, with many organelles, processes, and genes necessary for survival. Viruses, on the other hand, are much simpler, relying on the host cell for many essential functions.

* Coding Capacity: Viral genomes are streamlined to encode only the essential genes needed to replicate within a host cell. They lack the genes for basic cellular processes that eukaryotic genomes possess.

* Size Comparison: Eukaryotic genomes typically range in size from millions to billions of base pairs. Viral genomes, on the other hand, are usually only thousands to hundreds of thousands of base pairs.

Examples:

* Human Genome: Approximately 3 billion base pairs

* Influenza Virus: Around 13,500 base pairs

* HIV: Around 9,700 base pairs

Exceptions:

While most viruses have smaller genomes than eukaryotes, some exceptions exist. For instance, some viruses like the Mimivirus have genomes that are larger than some bacteria. However, these are still significantly smaller than typical eukaryotic genomes.