Dice Question Streamline Icon: https://streamlinehq.com

Close the gap for NRD(3LIN*_{Z/3Z})

Determine the precise asymptotic growth of the non-redundancy NRD(3LIN^*_{Z/3Z}, n) by closing the current gap between the lower bound Ω(n^{1.5}) and the upper bound ẐO(n^{1.6}).

Information Square Streamline Icon: https://streamlinehq.com

Background

The paper introduces new techniques connecting non-redundancy to matching vector families and proves bounds for the predicate 3LIN*_{Z/3Z}, obtaining Ω(n{1.5}) and ẐO(n{1.6}).

This gives the first example of a predicate with proven non-integer exponent growth for NRD, and tightening this to a precise exponent remains a central challenge.

References

Closing the gap between $\Omega(n{1.5})$ and $\widetilde{O}(n{1.6})$ for $NRD(3LIN_{Z/3Z}*, n)$ is a tantalizing open question.

— Redundancy Is All You Need (2411.03451 - Brakensiek et al., 5 Nov 2024) in Subsection “Technical Overview”