When a phrase ends with a period, do you put ... or .. after it?

Solution 1:

An ellipsis is always 3 dots. A period is always one dot. If you need both an ellipsis and a period, that totals up to 4 dots.

Chicago Manual of Style, 14th Edition, section 10.55:

When the last part of a quoted sentence is omitted and what remains is still grammatically complete, four dots—a period followed by three ellipsis dots—are used to indicate the omission.

Ideally the ellipsis would be set distinctly from the period, using for example the Unicode Horizontal Ellipsis codepoint (U+2026):

…

Although the CMoS indicates "period followed by ellipsis", I believe that sometimes the ellipsis may come before the period, depending on the nature of your sentence.