If p = mfBound M, then the p-th syzygy of M, which is computed by highSyzygy(M), should (this is a conjecture) be a "high Syzygy" in the sense required for matrixFactorization. In examples, the estimate seems sharp (except when M is already a high syzygy).
The actual formula used is:
mfBound M = max(2*r_{even}, 1+2*r_{odd})
where r_{even} = regularity evenExtModule M and r_{odd} = regularity oddExtModule M. Here evenExtModule M is the even degree part of Ext(M, (residue class field)).
The object mfBound is a method function.