On the performance of birthday spacings tests with certain families of random number generators

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An Object-Oriented Random-Number Package with Many Long Streams and Substreams (2002, background): “Other random number packages with multiple streams have been proposed in recent years; see for example Mascagni and Srinivasan (2000).”
TestU01: A C library for empirical testing of random number generators (2006, background): “This has the advantage of providing more points (a larger n, and usually a more powerful test) for a given number of calls to the generator [L’Ecuyer et al. 2002]. Marsaglia and Zaman [1993b] name these overlapping serial tests monkey tests: they view the generator as a monkey typing “random” charac”
PCG : A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation (2014, background): “[28], who observe that LCGs are only free of birthday-test issues if n < 16p1/3, where n is the number of numbers used and p is the period), we can surmise that wemay observe statistical flaws in a 128-bit LCG after reading fewer than 247 numbers (which is more than BigCrush consumes but nevertheles”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “Another family of tests that can be defined using the above setup is as follows [253].”