For the colors in table 3.5, the most dissimilar colors (as measured by distance in U*V*W* space are colors 1 and 3 in the diagram below, that is, red and green. The most similar are yellow (2) and white (7, not shown).
I also tested some other arbitrary colors to see if the distance measure matched my perceptual expectations. The colors tested are shown in the lower half of the figure below. The most dissimilar was again a reddish and a greenish (1 and 3), and the most similar was the two brownish colors (4 and 6), with a distance of 14. I would have thought that the two reds were most similar, but their distance in U*V*W* space was 33 (which is the second closest pair).
Here is an image of the colors in table 3.5 and some other colors I tested: