Landau Constants precision

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Looking at an article in Wikipedia on Landau constants it indicates that the actual values are not known except that they are within a certain interval. This seems surprising to me since for most constants, with enough computing power, one can calculate their values to any number of decimal places one wants. There is no explanation in the article as to why cannot do the same for Landau constants. Does anyone know the answer (for a non-expert).

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Well, to get a good approximation for $\pi$, say, you only need to measure a rope around a circle or compute a well-known series up to sufficiently many summands. The Landau constants, on the other hand, make a statement about a very large family of vary much varying functions ...