The excess of Hadamard matrices and optimal designs

Abstract Hadamard matrices of order n with maximum excess σ ( n ) are constructed for n =40, 44, 48, 52, 80, 84. The results are: δ (40)=244, σ (44)=280, σ (48)=324, δ (52)=364, σ (80)=704, σ (84)=756. A table is presented listing the known values of σ ( n ) 0 n ⩽100 and the corresponding Hadamard matrices are constructed. For the remaining values of n =56, 60, 68, 72, 76, 88, 92, 96 the largest values achieved for the excess are also given.