Dave wrote:
a parabolic reflector fed with a feedhorn. no 'elements', just a
hole in a pipe and a big curved plate. you need to define the
parameters a bit more.

OK, maximum gain for a single frequency, free space, sidelobes and
back-front ratio not important. Not concerned about number of elements -
only minimum total material length. Doesn't need to be rotatable - this
is a purely theoretical exercise.

Parabolic reflector sounds good but it's a bit hard to quantify for the
purposes of minimising total material length. Perhaps one could use a
wire mesh dish. Would that use more or less material than a Yagi? I
would imagine that a phased array radar could use the wire mesh approach
but the same questions would apply as for the parabolic reflector. Same
for corner reflectors.
Arrays of driven elements may be promising but the few such antennae
that I've simulated so far, use more material than Yagis for the same gain.

Alan