Bannai–Ito conjecture on metric and cometric association schemes

An association scheme is primitive if all of its associate graphs are connected; otherwise it is imprimitive. It is metric if its intersection numbers satisfy the metric vanishing conditions, and cometric if its Krein parameters satisfy the analogous conditions.

Bannai–Ito conjecture. For sufficiently large diameter, a primitive association scheme is metric if and only if it is cometric.

If true, this would imply that, for sufficiently large diameter, most of the Krein parameters of a primitive distance-regular graph vanish. The conjecture is attributed to Bannai and Ito; its resolution is not specified in the source.