Can a pdf give your iPhone a virus or put malware onto it?

I had received an email from someone I met over the internet and they were sending a pdf to me. I opened the pdf and it popped up of safari, I then saved it onto my notes, where I would click a link on my notes and the pdf would come up. Is this considered a download? If that pdf contained malware could it have infected my iPhone? I had block fraudulent sites and things like that, but I don't knoe if it would work on a PDF.

It COULD if you clicked on a link in that .pdf file.