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I have an experimental design where there are $b$ blocks and $k$ treatments. In each block there are $r$ replicates of each treatment in a random order. Let me illustrate this situation in the next table with $b=2$, $k=3$ and $r=2$, and where $t_i$ indicates that the treatment $i$ is used in the experimental unit:

\begin{array}{|c|c|c|c|c|c|c|} \hline \text{Block }1&t_2&t_1&t_1&t_3&t_2&t_3\\ \hline \text{Block }2&t_3&t_2&t_1&t_2&t_3&t_1\\ \hline \end{array}

What type of design of experiment is this?

This is not a randomized block design (RBD), since in a RBD there is just one replicate of each treatment.

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