https://nova.newcastle.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:28734 Wed 11 Apr 2018 12:10:08 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:26737 n/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, [forumal cannot be replicated]. By a recent result of Livinskyi, d²/h^1/2 → 0 as n → 8, so the second bound is close to (πe/2)^-d/2 for large n. Previous lower bounds tended to zero as n → ∞ with d fixed, except in the cases d ∈ {0, 1}. For d ≥ 2, our bounds are better for all sufficiently large n. If the Hadamard conjecture is true, then d ≤ 3, so the first bound above shows that R(n) is bounded below by a positive constant (πe/2)^-3/2 > 0.1133.]]> Wed 11 Apr 2018 10:30:42 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:13816 Tue 24 Aug 2021 14:28:05 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:28706 n has no proper Hadamard submatrix of order m > n/2. We generalize this result to maximal determinant submatrices of Hadamard matrices, and show that an interval of length ~ n/2 is excluded from the allowable orders. We make a conjecture regarding a lower bound for sums of squares of minors of maximal determinant matrices, and give evidence to support it. We give tables of the values taken by the minors of all maximal determinant matrices of orders ≤ 21 and make some observations on the data. Finally, we describe the algorithms that were used to compute the tables.]]> Sat 24 Mar 2018 07:30:08 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:26948 Sat 24 Mar 2018 07:27:02 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24828 Sat 24 Mar 2018 07:15:13 AEDT ]]>