Spectral test
![Three-dimensional plot of 100,000 values generated with RANDU. Each point represents 3 consecutive pseudorandom values. It is clearly seen that the points fall in 15 two-dimensional planes.](/Images/godic/202502/12/Randu4503.png")
The spectral test is a statistical test for the quality of a class of pseudorandom number generators (PRNGs), the so-called linear congruential generators (LCGs). As this test is devised to study the lattice structures of LCGs, it can not be applied to other families of PRNGs. According to Donald Knuth, this is by far the most powerful test known, because it can fail LCGs which pass most statistical tests. The IBM subroutine RANDU LCG fails in this test for 3 dimensions and above.