Maximal partial spreads in PG(3,4) and maximal sets of mutually orthogonal Latin squares of order 16 (Q1861303)

A set \(M\) of \(r\) mutually skew lines of \(\text{PG}(3,q)\) is called a maximal partial spread of size \(r\) if any other line of \(\text{PG}(3,q)\) meets some line of \(M\). Recently, Leonard Soicher classified all maximal partial spreads of \(\text{PG}(3,4)\) up to projective equivalence via computer search, see the internet link \url{http://www.maths.qmw..ac.uk/~leonard/partialspreads/}. As it turns out, there are exactly twenty-nine maximal partial spreads (up to equivalence): six of size 11, three of size 12, thirteen of size 13, four of size 14, and three of size 17. Each maximal partial spread of \(\text{PG}(3,4)\) of size \(r\) gives rise to a translation net of order 16 and degree \(r\) and hence to a set of \(r-2\) mutually orthogonal Latin squares of order 16.