Tight Lower Bound for Average Number of Terms in Optimal Double-base Number System
Vorapong Suppakitpaisarn
TL;DR
This paper establishes a tight lower bound on the average number of terms in the optimal double-base number system, matching previous upper bounds and advancing understanding of its efficiency.
Contribution
It proves a matching lower bound of Omega(n / log n) for the average number of terms, confirming the optimality of existing upper bounds.
Findings
Lower bound of Omega(n / log n) for average terms
Matching previous upper bounds from 2008
Advances theoretical understanding of double-base number systems
Abstract
We show in this note that the average number of terms in the optimal double-base number system is in Omega(n / log n). The lower bound matches the upper bound shown earlier by Dimitrov, Imbert, and Mishra (Math. of Comp. 2008).
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Taxonomy
TopicsAlgorithms and Data Compression · Cryptography and Residue Arithmetic · Coding theory and cryptography