Stratis Kounias

Best Linear Bonferroni Bounds

Consider the probability space

The exact D-optimal first order saturated design with 17 observations

(S,F,P)

The maximum determinant of 21×21 (+1, −1)-matrices and d-optimal designs

and the sequence of events

Supplementary difference sets and optimal designs

A_i \in F,i = 1,2, \cdots ,n

Supplementary difference sets and D-optimal designs for n ≡ 2 mod 4

; the problem is to evaluate, under limited information, the probability of an event A defined thro...

The excess of Hadamard matrices and optimal designs

Abstract The exact D-optimal first order saturated design with 17 observations is given. The upper bound of the determinant of the information matrix is established and a design attaining this value is constructed. The information matrix is proved to be unique and the optimal design contains the B.I.B. design (16, 16, 6, 6, 2).

On the excess of Hadamard matrices

The 21×21 (+1, −1)-matrix R∗ with the maximum determinant is given. An algorithm is developed to find all 21×21 matrices M with determinant the square of an integer and ⩾(det R∗)2, where M=(mij), symmetric, positive-definite, mii=21, mij≡1 mod 4, i≠j. There are found, besides M∗=R∗TR∗, two more such matrices M1, M2 and then the non-existence of Ri such that R1TR1 = M1, R2TR2 = M2 is proved.

Some d-optimal weighing designs for n≡ (mod 4)

Abstract D-optimal designs of order n = 2 v ≡ 2 (mod 4), where q is a prime power and v = q2 + q + 1 are constructed using two methods, one with supplementary difference sets and the other using projective planes more directly. An infinite family of Hadamard matrices of order n = 4v with maximum excess σ(n) = n n−3 where q is a prime power and v = q2 + q + 1 is a prime, is also constructed.

On sequences with zero autocorrelation

Supplementary difference sets 2{12n; k, r; λ} are used to construct D-optimal designs for n ≡ 2 mod 4, where k, r, λ are defined through n. A number of new designs is constructed. The D-optimal design for n ≡ 86 is constructed for the first time. For n ≡ 2 mod 4, n<100 and for the cases n = 22, 34, 58, 70, 74, 78, 90, 94, 98, the D-optimal designs still remain unknown.

On base and Turyn sequences

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.