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