  Recent works of Costa-Dalai, Christandl-Gesmundo-Zuiddam,
Blatter-Draisma-Rupniewski, and Bri\"et-Christandl-Leigh-Shpilka-Zuiddam have
investigated notions of discreteness and gaps in the possible values that
asymptotic tensor ranks can take. In particular, it was shown that the
asymptotic subrank and asymptotic slice rank of any nonzero 3-tensor is equal
to 1, equal to 1.88, or at least 2 (over any field), and that the set of
possible values of these parameters is discrete (in several regimes). We
determine exactly the next gap, showing that the asymptotic subrank and
asymptotic slice rank of any nonzero 3-tensor is equal to 1, equal to 1.88,
equal to 2, or at least 2.68.
