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Tromp and Farneback do not provide any error margins on the numbers of positions for square boards larger than 17x17. However, they do give a significancy of 4 digits for the 19x19 as opposed to up to 2 for the other square boards.
I am curious whether the heuristic used realy gives an error margin of the order of less then 1 promile. Since it is a heuristic, i would like more evidence of the error margin.
They actually give a more accurate estimate on page 28, where they say:
This number was arrived at not through simulation, but through a converging ratio of legal positions between square and almost square boards. The number:
L(n,n) x L(n+1, n+1)
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L(n, n+1)^2
(where L(X,Y) is the number of legal positions on an X x Y board)
converges very rapidly for growing n, and can be used to accurately estimate the number of legal positions.