I'm not a big fan of assertNot() and tend to experience unexpected things that can happen to SUT, not to mention testing them in addition to the normal Assert in each individual test.
IMO, you should only check the nominal status of your facilities. If in some cases it is normal for someVal be null, create a special test method to verify that it is indeed null in this scenario. For your test, select a name that indicates the intent, for example someValShouldBeNullWhen...() . Do the same for empty or any other value.
You see that unexpected things happen to your SUTs by looking at your test exception messages, rather than trying to predict each of these unexpected things in advance and interrupt your tests with assertNots for them.
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