How is the $L^2$ norm of the solution from an integer relation algorithm (read: PSLQ) distributed for integer inputs? Common factors among the inputs to PSLQ may have to be taken into consideration.
Put another way, I have a fixed integer vector $u$ to be dotted with an integer vector $v$ with $0<|v|
I ran some Monte Carlos, and compared actual results from PSLQ to a model assuming dot products are normally distributed, using an observed variance. In almost every case the solution from PSLQ was estimated to be smaller than 100% of random solutions, or larger than 100% of random solutions. Very frustrating but even more intriguing than frustrating!