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

摘要

The maximal partial spreads of PG(3,4) were recently classified by Leonard Soicher. Each such partial spread (with r lines, say) yields a translation net of order 16 and degree r and hence a set of r-2 mutually orthogonal Latin squares of order 16. We determine which of these nets are transversal-free. In particular, we obtain sets of t MAXMOLS(16) for two previously unknown cases, namely for t = 9 and 10.