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HO-229 does not promise 0.1'  accuracy in final product, though I can see that it is easy to infer that it does.  The point of HO-229 and the Nautical almanac having 0.1' precision is to minimize the cumilative error in the final product, i.e. an LOP.  Working sights to the nearest 0.1' will not give you 0.1' accuracy because some of the values used do not have that good a precision, such as Hs which has precision near 1.0' due to the variable horizon.  There are a fair number of values in working a sight reduction and if you can limit the number that have precision near 1.0' you can improve your odds for occasionally having most or all of these values have their errors line up one way or the other.resulting in a large error.

Re: Optimal HoE?
From: Bob Goethe
Date: 2019 Aug 19, 12:25 -0700

. . . 

I had in the past seen an irregular horizon and assumed it was waves.  The idea that it might be due to irregular refraction (presumably there are parcels of air that have different temperature and humidity between me and the horizon, all bending light slightly different) was an eye-opener for me.

This has made me wonder about the usefulness of Pub. 229 compared to Pub. 249.  Sure, 229 promises tenth-of-a-minute accuracy, but is this a deceptive promise, in light of irregular refraction right at the horizon?  That is, does Pub. 229 promise more than it could ever deliver?

Thanks.

Bob