Paired Subset Selection with Randomization

Here is what I am trying to execute:
I have 2 designs (we will call them A & B ), each of which I am comparing to 19 other designs in paired comparisons. The respondent will rank each pair on a sliding scale from 0 (completely different) to 100 (identical). Rather than having each respondent go through all 38 pairs, what I would like to do is be able to have the block randomly select 10 of the 19 pairs with design A and 10 of the 19 pairs with design B to show the respondent. The thing is, I need the selected A-to-other design comparisons to be the same "other designs" as the B-to-other design comparisons in order to analyze the data comparatively. And, the block needs to be entirely randomized, showing the selected 20 pairs in random order. Is there a way to execute this?