Reproduction of the same luminance value on the display

HI, all.

I have a question about how to project an image created with Radiance.
I am trying to project an image on a LED display and reproduce the same luminance value as in the actual space. The LED display can output up to 1200 cd, but only supports up to 8-bits.

First, I shot a space with a maximum luminance of 1200 cd and created an HDR image. After that, I converted it to tiff format while performing gamma correction.
However, when projected images, the luminance value is about 3 times the actual.
The following is the command used.

normtiff -d 2400 -u 1200 -g 2.2 output.hdr output_display.tif

When I entered this command, I confirmed that -d determined the luminance of the image.
How should I set the -d parameters if I want to reproduce the same brightness on the ?

I would appreciate it if you could tell me if there is another way.
Thanks in advance.