Limits RegistryPUBLIC RECORDLimits RegistryResearch Console →Classical sphere-packing upper bound on the reliability exponent above critical rate.
The question, scope, and sources behind this Registry record.
Bound the best achievable exponential decay rate of decoding error for a discrete memoryless channel at rate R.
Current frontiers derived from accepted Claims.
Assertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
No accepted machine-checked reproductions are recorded for this Limit.
Limits Registry. LR-003219. Sphere-packing converse for discrete memoryless channels. 2026.