Bounded Additive Relation and Application to Finite Multiple Zeta Values

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 $10$.