  A honeycomb array is an analogue of a Costas array in the hexagonal grid;
they were first studied by Golomb and Taylor in 1984. A recent result of
Blackburn, Etzion, Martin and Paterson has shown that (in contrast to the
situation for Costas arrays) there are only finitely many examples of honeycomb
arrays, though their bound on the maximal size of a honeycomb array is too
large to permit an exhaustive search over all possibilities.
  The present paper contains a theorem that significantly limits the number of
possibilities for a honeycomb array (in particular, the theorem implies that
the number of dots in a honeycomb array must be odd). Computer searches for
honeycomb arrays are summarised, and two new examples of honeycomb arrays with
15 dots are given.
