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Probabilistic lower bounds on maximal determinants of binary matrices

Brent, Richard; Osborn, Judy-Anne; Smith, Warren D.


et D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/nn/2 be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on D(n) and R(n) in terms of d = n − h, where h is the order of a Hadamard matrix and h is maximal subject to h ≤ n. For example, (Formula Presented) By a recent result of Livinskyi, d2/h1/2 → 0 as n → ∞, so the second bound is close to (πe/2)−d/2 for large n. Previous lower bounds tended to zero as n→∞with d...[Show more]

CollectionsANU Research Publications
Date published: 2016
Type: Journal article
Source: Australasian Journal of Combinatorics
Access Rights: Open Access


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