Two limitations on the model of a relation that we may pursue are evident: (i) the length of the vector aand (ii) the precision to which the entries of the vector a are known. As a rule of thumb, if a has n entries and D is the maximal number of digits among the entries of c, then (as an easy counting argument shows) we have to know all entries of the vector a to the precision somewhat greater than nD digits and computations have to be performed using at least this level of numeric precision, if we hope to be able to distinguish between bogus and significant relations c.
Since different integer relation algorithms (and their implementations) can differ by as much as two orders of magnitude in their running times on the same input, there are no globally valid limitations on n and D. In Section 4 we include timings and the required precision for an example with n=31, D=6 and running times ranging between dozens of seconds and dozens of minutes for various implementations. The largest example that we have run was with an input vector aof length 171, given with a precision of 2000 decimal places; a total of 56 linearly independent integer relations (with few digit coefficients) were recovered in 7 days of CPU time on a DEC Alpha station (Section 3.2).