What does Antigone claim is the worst kind of death? Why does she say this?

In Antigone, Antigone says that the worst kind of death is a death without honor.  She believes that the laws of the gods trump the laws of men.  As such, the gods hold that family members need to honor their dead, so even though Creon the king has ordered that Polynices not be buried because he is a traitor, Antigone believes that Polynices deserves a proper burial because he is her family member.  Antigone, like the other citizens in Thebes, knows that Creon has ordered the punishment of death on anyone who attempts to bury the body of Polynices, but she believes that the laws of the gods trump those of men.  She cannot bear the thought of going to her grave as a dishonorable woman--one who has not obeyed the laws of the gods.  So she opts for a death with honor and buries her brother.