Is there a 9×9 Sudoku Room Square?

Question

The following is an order 9 Room square. Copying from Wikipedia,

1. Each cell of the array is either empty or contains an unordered pair from the set of symbols.
2. Each symbol occurs exactly once in each row and column of the array.
3. Every unordered pair of symbols occurs in exactly one cell of the array.

This square meets a few additional requirements, each $3\times3$ square has five pairs, and a few of the squares have all ten symbols.

Is an order 9 Room square possible where all nine $3\times3$ squares have all ten symbols?

Note: I don't think row/column permutations for this particular Room square will yield an answer, due to trying a few million cases.

Answer 1

Yes, it is possible. Here is the first solution found by a simple search algorithm. \begin{array}{|ccc|ccc|ccc|}\hline 01&23&45&67&89&&&&\\ 68&79&&02&&&14&35&\\ &&&15&34&&78&06&29\\ \hline 25&&&39&07&18&&&46\\ 37&16&08&&&24&59&&\\ 49&&&&56&&03&28&17\\ \hline &04&69&&12&57&&&38\\ &58&13&&&09&26&47&\\ &&27&48&&36&&19&05\\ \hline \end{array}