What is the strongest R-value?

The strongest R-value per inch among commercially available insulation materials is found in vacuum insulated panels, which can achieve R-25 to R-50 per inch at the center of the panel, and in aerogel insulation which achieves about R-10 to R-10.3 per inch. Among more conventional and widely used building insulation that can be cut and installed on a job site, the highest R-value per inch is phenolic foam board like Kingspan Kooltherm at about R-8 to R-8.5 per inch, followed by polyisocyanurate rigid foam at R-6 to R-6.5 per inch, and closed-cell spray foam at R-6.5 to R-7 per inch. In terms of total assembly R-value, you can stack materials to achieve essentially unlimited R-value, for example 12 inches of closed-cell spray foam would be R-78, and double-stud walls with dense-pack cellulose can reach R-40 to R-60. There is no absolute maximum R-value, you can keep adding layers, but beyond about R-60 in an attic or R-40 in walls the energy savings become very small compared to cost. So the strongest practical R-value is usually achieved by combining air sealing with high-performance foam and continuous exterior insulation.