AFAIK, in Java implicit constructors are always generated for a class without constructors [1], [2].
But in bytecode I could not find such restriction on the JVMS.>
You've already answered the question yourself: a class without a constructor is absolutely valid according to JVMS. You cannot write such a class in pure Java, but it can be constructed using bytecode generation.
Think of interfaces: they are also classes without a constructor from JVM point of view. And they can also have static members (you can even invoke interface's main method from the command line).