Abstract:
Let 
denote the finite field with 
elements,
for q being a prime power. may be regarded as an
n-dimensional vector space over 
. 
generates a normal basis for this vector space
(
), if
are linearly
independent over . Let N(q,n) denote the number of elements in
that generate a normal basis for ,
and let 
denote the frequency of such
elements.
We show that there exists a constant c>0 such that
and this is optimal up to a constant factor in that we
show 
We also obtain an explicit lower bound: 
Available as PostScript, PDF, DVI.