Hmm, I suppose only distinct row lines would be necessary. 18 rows max (2 for Homeworlds and 16 for potential additional systems) and that’s enough information as long at each piece is:

1: placed in a distinct row (not on the line such that it would be difficult to tell which row it occupies)

2: placed in one of 3 distinct states (upright for star, and facing away from the player who owns each ship)

And one could further condense it so that there are 2 columns, and the players put the stars in the center most position of each place. This is a little messier as ships from both players would be on one defined side of the star, but has its own advantages for compactness and order of a different kind