We formulate an algebraic problem to find a generating system of a finite subset of an Abelian group with respect to linear relations whose coefficients are bounded by a constant, and recall MITM algorithm for the problem. As an application of MITM algorithm for the Abelian group \begin{ eqnarray*} \mathbb{ Z}/106700590455862347842907841856033238416352421 \mathbb{ Z} \end{ eqnarray*} combined with Chinese remainder algorithm, we give a table of expected linear relations of finite multiple zeta values of weight $10$.
Categories: math.NT