A maximal arc of degree 
in the finite projective plane 
is a set 
of points
such that every line meets 
in either 0 or 
points. Necessarily,
 |
and 
divides 
. Nontrivial maximal arcs exist only when 
is even.
Alderson and Ball (2026) study a higher-dimensional generalization consisting of 
-dimensional subspaces
of the projective space 
with at most 
members in any hyperplane.
They prove
 |
and characterize equality. For 
this specializes to the maximal-arc bound after field reduction.
