Existence of an example in the final parameter case

Determine whether there exists a set A satisfying the parameter conditions 3 + 20 < 12, >, < -1, and 2 >, thereby providing an example for this case.

Background

The examples section presents instances for several mutually exclusive cases arising in the paper’s formula for the Frobenius number. The authors explicitly omit one case, characterized by the displayed inequalities 3 + 20 < 12, >, < -1, and 2 >. The stated difficulty is not merely that an example was omitted: the author reports being unable to find any set A corresponding to the case, leaving the existence of such an example unresolved in the paper.

References

However, no example is provided for the cases where:\ 3 + 20 < 12, > , < -1 and 2 >

The reason for this is that the author has not been able to find any set A corresponding to this case.

— A fast algorithm for the Frobenius problem in three variables  (2501.01099 - Rosin, 2 Jan 2025) in Section 5, Examples, immediately before Example 1