Let π be a finite projective
plane of order n. Recall that a blooking set lS in π is a set of points which does not
contain any line but which does intersect every line of π. The first objective is to
elaborate on the connection, pointed out by the writers, between blocking sets and
complete k-arcs of π. For example, the set of secants of a complete k-arc with
k < n + 2 dualizes to a blocking set. Using some simple observations, it is shown that
a blocking set in a projective plane π of order ten, if π exists, contains at
least 16 points. The proof uses a computer result on the nonexistence of
complete 6-arcs of π due to R. H. F. Denniston. Using the result, a recent
theorem concerning certain codes related to π due to MacWilliams, Sloane, and
Thompson is easily established. The result also shows that, in effect, a setof four mutually orthogonal latin squares of order ten is embeddable in acomplete set in at most one way. This improves slightly on the bound of R. H.
Bruck.
