By means of the method of the Laurent interpolation determinant, it is proved that, if ζ is an algebraic number, the real numbersd andL satisfy the inequalitiesd≥degζ,L≥L(ζ), andL≥3, and the numberd is sufficiently large, then the inequality $$|\pi - \varsigma | \geqslant \exp ( - 21.4708d \cdot (\log L + d \cdot \log d) \cdot (1 + \log d))$$ holds. The constant 21.4708 in the above estimate for the measure of transcendence of the number π is the best among the known values.