How to determine the number of items needed to design a reliable test

An educational assessment form equivalence problem.

I produce a large (infinite?) pool of items similar in quality. I administer a test that uses items from the pool. For each testee, items are drawn at random from the pool. The testees respond to x number of items.

If I need a reliability coefficient* of .90 or higher, what is x?

Is this even the question I should be asking?

*Found using the Spearman-Brown prediction formula, I assume?