Small Latin arrays have a near transversal

A Latin array is a matrix of symbols in which no symbol occurs more than once within a row or within a column. A diagonal of an n × n array is a selection of (Formula presented.) cells taken from different rows and columns of the array. The weight of a diagonal is the number of different symbols on it. We show via computation that every Latin array of order (Formula presented.) has a diagonal of weight at least (Formula presented.). A corollary is the existence of near transversals in Latin squares of these orders. More generally, for all (Formula presented.) we compute a lower bound on the order of any Latin array that does not have a diagonal of weight at least (Formula presented.).