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Even if you manage to convert it to a bitmap vector or eps / AI format, resizing will still affect the pixels as the image wasn't created as a vector in the first place. MrTom's suggested settings are excellent but it can only go so far to improve and maintain quality.

Unless you'ld be using the image in a vector application like Illustrator or even Corel Draw which can use scalable, converted to bitmap images. Even then, the quality is slightly affected.

Your original is not at a high resolution. You can try increase the original image's resolution while maintaining its size before sizing it down. And using a bit of sharpening.

But there's one thing you shouldn't forget... zooming up close will show the jaggedness. At normal view it will look fine. It's not like you'll be using the resized image magnified.