This is table about "Image file formats supporting indexed color". I don't see JPEG file format in this table.
Why doesn't JPEG file format follow indexed color technique?
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Besides Knut’s argument that indexed color cannot represent color gradients well, we can also look a the compression method.
The JPEG compression relies on similarity between neighboring pixel colors. In an indexed image, slightly changing the value of a pixel means picking a different color from the table, which could mean showing a completely different color. In contrast, slighting changing the pixel values in a full-color image only slightly changes the color. JPEG slightly changes the pixel values so that it can encode groups of them with fewer bits than it would take to encode them directly. You just cannot do this with an indexed color image.