Let 
be the set of all sequences that contain all sequences 
where 
and all other 
, and define
Then the merit factor problem requires the minimization of 
over 
for a fixed 
.
For 
,
2, ..., the first few minima are 5, 10, 18, 27, 43, 52, 72, ... (OEIS A091386).
This problem is known to be very hard, but is not known to be in one of the recognized combinatorial classes like NP (Borwein and Bailey
2003, p. 6).
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References
Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A
K Peters, 2003.Borwein, P. B. Computational
Excursions in Analysis and Number Theory. New York: Springer-Verlag, 2002.Sloane,
N. J. A. Sequence A091386 in "The
On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Merit Factor Problem
Cite this as:
Weisstein, Eric W. "Merit Factor Problem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeritFactorProblem.html
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