Tenses

[gurpreet]

Plese tell me if the following sentence is correct:

Neither Daphne's night case nor the other night cases we checked in the dorm have contained the missing necklace.

Shouldnt have contained be replaced by contained or had contained

Thanks

[Rusty]

Neither Daphne's night case nor the other night cases we checked in the dorm have contained the missing necklace.

Shouldnt have contained be replaced by contained or had contained

(It should be the simple past tense, contained).