Perfect Single Error-Correcting Codes in the Johnson Scheme

Delsarte conjectured in 1973 that there are no nontrivial pefect codes in the Johnson scheme. Etzion and Schwartz recently showed that perfect codes must be k-regular for large k, and used this to show that there are no perfect codes correcting single errors in J(n,w) for n les 50 000. In this correspondence we show that there are no perfect single error-correcting codes for n les 2²⁵⁰