My standard design for map bases is a piece of 1/4″ (0.6 cm) luan plywood with a frame of 1×2 (2.5 cm x 5 cm) lumber on edge glued and nailed around the underside edges.
This time around, instead of using 1x2s for the edges, I cut strips of 3/4″ (2 cm) plywood since I had a bunch of scraps leftover from some shelves I built for my classroom.
Given how wide these maps are, I decided to add a third central strip along undersides to help stiffen the bases.

Unfortunately, this was not enough. While the bases did a good job of resisting being bent along their lengths and widths, they were still easily twisted.
I tried adding a set of cross supports…

But this didn’t really help. The bases could still easily have one corner lifted up while the other three corners remained on the ground.

The solution here was to add diagonal cross-bracing. With these pieces in place, each base is nicely rigid and acts like a single large slab of wood.

When adding these extra support pieces, I planned ahead for my potential need to string wires from place to place under the bottom. Rather than have to drill a bunch of holes each time I needed to string a wire from one side of a support to the other, I made all my supports a little thinner than the edge pieces so that even when the map was flat on a table, there would be room between the supports and the table for the wires to fit.
Unfortunately, I didn’t think of this when installing my original extra support in the center. Those pieces were the same thickness as the sides.
To fix this, I used a hand plane to shave down the central stiffening ribs to the same height as the rest.

A little sanding, and the bases were all done.