Abstract
Two ways of constructing maximal sets of mutually orthogonal Latin squares are presented. The first construction uses maximal partial spreads in PG(3, 4) b PG(3, 2) with r lines, where r ∈ l6, 7r, to construct transversal-free translation nets of order 16 and degree r + 3 and hence maximal sets of r + 1 mutually orthogonal Latin squares of order 16. Thus sets of t MAXMOLS(16) are obtained for two previously open cases, namely for t e 7 and t e 8. The second one uses the (non)existence of spreads and ovoids of hyperbolic quadrics Q+ (2m + 1, q), and yields infinite classes of q2n − 1 − 1 MAXMOLS(q2n), for n ≥ 2 and q a power of two, and for n e 2 and q a power of three.
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