A158865 Smallest maximal excess attained by an equivalence class of Hadamard matrices of order 4n.

0, 8, 20, 36, 56, 80, 108, 140

Offset: 0

Author

William P. Orrick, Mar 28 2009

Keywords

• hard
• more
• nonn

Comments

The excess of a {-1,1} matrix is the sum of its elements. The maximal excess of an equivalence class of Hadamard matrices (cf. A007299) is the largest excess attained by a member of the class. The largest maximal excess of any equivalence class is given by A004118.

Examples

			All equivalence classes in orders 20 and 28 attain the same maximal excess. In order 16, three classes attain maximal excess 64 and two attain maximal excess 56. In order 24, 56 equivalence classes attain maximal excess 112 and four attain maximal excess 108.
		

References

• Best, M. R. The excess of a Hadamard matrix. Nederl. Akad. Wetensch. Proc. Ser. A {80}=Indag. Math. 39 (1977), no. 5, 357-361.
• Brown, Thomas A. and Spencer, Joel H., Minimization of +-1 matrices under line shifts. Colloq. Math. 23 (1971), 165-171, 177 (errata).
• R. Craigen and H. Kharaghani, Weaving Hadamard matrices with maximum excess and classes with small excess. J. Combinatorial Designs 12 (2004), 233-255.

Formula

For bounds on a(n), see A004118.