## 4 Experimental Results  
In this section, we report on experimental results by applying the proposed framework to Base45 and Base85 encodings: as previously said, the set \(\mathbf{E}^{\prime}\) is built with \(\varphi\) assuming a uniform distribution of the \(2^{n}\) binary strings. This choice was made because it is general and makes no assumptions on the possible distribution of the binary strings: we will discuss the possibility to increase the payload with \(\varphi\) mapping on the set of the most probable sequences in \(\mathbf{C}\) for specific domain contexts, like encodings of TIFF or JPEG images. Anyway, we tested three different mappings called Map 1, Map 2 and Map 3. When Map 1 is used the set \(\mathbf{E}^{\prime}\) consists of the sequences mapped to the \(a^{s}-2^{n}\) binary strings counting from \(\left\{0\right\}^{n}\) with an increment of \(\left\lfloor 2^{n}/\left(a^{s}-2^{n}\right)\right\rfloor\). Map 2 maps the sequences in \(\mathbf{E}^{\prime}\) to the first \(a^{s}-2^{n}\) binary strings while Map 3 puts in correspondence \(\mathbf{E}^{\prime}\) with the last \(a^{s}-2^{n}\) binary strings. Tables 2-4 report the averaged results from embeddings using Base45 and Base85 encodings into a set of 500 colour images of size \(768\times 576\) in JPEG, TIFF and PNG formats, respectively. The first column reports the string encoding, the second and third columns report the average payload in bpb and in bps, respectively. The fourth column reports the used mapping, while the fifth column reports when the experimental average payload is greater (+, ++) or less (\(-\), \(--\)) than the expected one. As it can be seen from the values shown in columns 2 and 3, the results are in line with the expected theoretical values (\(p\) and \(q\)) computed in the previous section. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Base**} & **Average (\(\pm\)std dev)** & **Average (\(\pm\)std dev)** & & **Comparison** \\  & **Payload per Input Byte** & **Payload per Output** & **Map** & **with Expected** \\  & **[bpb]** & **Symbol [bps]** & & **Payload** \\ \hline Base45 & \(0.19905\pm 0.00415\) & \(0.13270\pm 0.00277\) & \(1\) & \(+\) \\ Base45 & \(0.19820\pm 0.00397\) & \(0.13213\pm 0.00265\) & \(2\) & \(+\) \\ Base45 & \(0.19208\pm 0.00371\) & \(0.12805\pm 0.00247\) & \(3\) & \(--\) \\ Base85 & \(0.00838\pm 0.00029\) & \(0.00670\pm 0.00024\) & \(1\) & \(+\) \\ Base85 & \(0.00915\pm 0.00080\) & \(0.00732\pm 0.00064\) & \(2\) & \(++\) \\ Base85 & \(0.00733\pm 0.00067\) & \(0.00586\pm 0.00054\) & \(3\) & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the Base45 and Base85 encodings applied to 500 JPEG image (average image size 109 KB). In almost all cases, Map 1 and Map 2 mappings result in a higher average payload than the expected one for image files. It should be pointed out that for Base85, Map 2 mapping behaves quite differently for TIFF compared to PNG image formats: in the former case, the average payload is much greater (\(\sim 1.55\) times) than the expected one, while in the latter is much smaller (0.84 times). Similar results for compressed files (in.zip,, bz2,.gz and.tgz formats) of various sizes are reported in Tables 5-8. By contrast with the image case, it seems that the best mapping depends on the compressed file format: for.zip and.bz2 file format, Map 1 and Map 2 give better payload than expected, while for.gz file format Map 3 is the best.