Just noticeable quantization levels, which are conventionally used in picture coding, have been mainly developed for standard 8-bit images and low dynamic range (LDR) typical screens. The quantization levels however have not been adapted yet for high dynamic range (HDR) imaging and its accompanied HDR displays, which can reach up to a peak luminance of 4000 cd/m(2). This study proposes an experimental methodology on UDR displays to determine just noticeable quantization levels for discrete cosine transform (DCT) coefficients on high luminance images. In the first stage of the proposed method, the quantization noise patterns for different DCT frequencies at different mean luminances are rendered by predicting the LED and LCD values of the two layer HDR display. Then, a two alternative forced choice based psychovisual experimental procedure using geometric search and QUEST methodology is realized by randomly presenting the rendered quantization noise at different amplitudes to the subjects in order to determine the just noticeable levels. The experiments are performed over 3 subjects for 30 different frequencies of 8x8 DCT patterns at mean luminances of 100 cd/m(2) and 1000 cd/m(2). The results are interpreted with respect to frequency and luminance changes and from the point of utilized methodology, namely geometric search and QUEST.