The 25th Amendment, not the Presidential Succession Act of 1947, covers when the VP becomes President or Acting President. The PSA covers the rest, but there are questions regarding its Constitutionality (search “Presidential Succession Act” and “unconstitutional”).
I have read the 25th amendment, but I don’t see what happens if the President and VP are both killed.
Amendment XX provides that Obama and Biden’s terms end and the newly elected Pres and VP terms begin Jan 20 at noon. It also says Congress shall provide for the case if neither Pres nor VP are qualified.
Article II Section 1 provides that “before he enter on the execution of office”, he shall take the oath.
So if President Elect and VP Pence were to be killed either before or after the oath it looks to me like whatever law Congress has passed would apply.
All I can say is at least it wouldn’t be a democrat, unless the Top Senate leaders are also taken out.