On the Number of Defects in Optimal Quantizers on Closed Surfaces: The Hexagonal Torus

Key Points

• Defects in optimal quantizers on the hexagonal torus surface can significantly influence data representation.
• Quantization errors of up to 15% were noted, impacting the overall efficiency of data encoding.
• Analysis using geometric principles on closed surfaces unveils challenges in optimal quantization techniques.
• Understanding defects in this context may enable advancements in fields like data compression and signal processing.