  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 $n\times n$ array is a
selection of $n$ 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 $n\le11$ has a diagonal of weight
at least $n-1$. A corollary is the existence of near transversals in Latin
squares of these orders.
  More generally, for all $k\le20$ we compute a lower bound on the order of any
Latin array that does not have a diagonal of weight at least $n-k$.
