The filtered laser excitation technique was applied for measuring transition frequencies of the Ca$_2$ B-X system from asymptotic levels of the X$^1Sigma_{mathrm g}^{+}$ ground state reaching $v=38$. That level has an outer classical turning point of about 20~AA which is only 0.2 rcm below the molecular $^1$S$+^1$S asymptote. Extensive analysis of the spectroscopic data, involving Monte Carlo simulation, allowed for a purely experimental determination of the long range parameters of the potential energy curve. The possible values of the s-wave scattering length could be limited to be between 250$a_0$ and 1000$a_0$.
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