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Depends on the pixcel resolution of the autoguider and the how the autoguider detects error signals (full pixcel, 1/2 pixcel, 1/3 pixcel , 1/4 pixcel or less or more) and if you are using the big scope only at prime focus or via a barlow or eyepiece too.
I am only guessing , but I would expect the guidescope needs a focal length not less than 1/2 that of the main scope.
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