Graphical t-wise balanced designs

t-Wise Balanced Designs

Steiner 3-wise balanced designs are constructed for parameters 3-(3n − 1, {4, 8}, 1), 3(qnm− qm, {q− 1, q, q+ 1}, 1), 3-(qnm− 2qm− 1, {qm− 3, qm− 2, qm− 1, qm, qm+ 1}, 1), 3-(qnm − 2qm, {qm − 3, qm − 2, qm − 1, qm, qm + 1}, 1), 3-(qnm − 2qm + 1, {qm − 3, qm − 2, qm−1, qm, qm+1}, 1), where q is a prime power and n ≥ 2, m ≥ 1 are integers. Further designs are obtained from these. © 2008 Elsevier ...

Constructing t-designs from t-wise balanced designs

We give a construction to obtain a t-design from a t-wise balanced design. More precisely, given a positive integer k and a t(v, {k1, k2, . . . , ks}, λ) design D, with with all block-sizes ki occurring in D and 1 ≤ t ≤ k ≤ k1 < k2 < · · · < ks, the construction produces a t-(v, k, nλ) design D∗, with n = lcm( ( k1−t k−t ) , . . . , ( ks−t k−t ) ). We prove that Aut(D) is a subgroup of Aut(D∗),...

A Fisher type inequality for weighted regular t-wise balanced designs

Delsarte and Seidel found that the dimension of a certain linear space can serve as a Fisher type lower bound for the size of a weighted regular t-wise balanced design. They put it as a problem to explicitly determine this dimension. This note calculates the rank of a special set inclusion matrix and then solves the above problem.

Constructions of 3-resolvable nested 3-designs and 3-wise balanced designs

Balanced Nested Designs and Balanced n-ary Designs

We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (1972). By use of these constructions, we show some constructions for regu...