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).

## Explore with Wolfram|Alpha

## 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

## Subject classifications