On finding the exact values of the constant in a $(1,q_2)$-generalized triangle inequality for Box-quasimetrics on $2$-step Carnot groups with $1$-dimensional center

For $2$-step Carnot groups with $1$-dimensional center, a method for defining the exact values of the constant $q_2$ in a $(1,q_2)$-generalized triangle inequality for their Box-quasimetrics is developed. The exact values of the constant $q_2$ are defined for $4$-, $5$-, and $6$-dimensional $2$-step Carnot groups with $3$-dimensional horisontal subbundle.