A shiny finish can be obtained by following the steps described below:
First, sand with using a 400 grit index disk. Then, keep sanding with water and finer grits (600,800, voir 1000...), in order to get rid of all the smaller/micro scratches still left on the board.
For a perfect finish, take the time to do another hot-coating (or ''gloss''), using a brush to spread some low viscosity resin (paraffined resin + catalyst), on each side of the board. Let it dry. Then, sand the board again with water and a grit index of 400, gradually going up to 800 or more.
With your sanding machine, featuring a polishing plate in genuine sheep skin, and some polish, keep working on the board, in circular movements, until you reach the desired outcome. Use a moderate speed of rotation of the sander, in order to avoid any over-heating.
Finally, protect your work with a finish liquid, and a synthetic lustring disk, with a tolerance to higher rpm.
These additional steps will guarantee the best mirror effect you can obtain !