t-Wise Balanced Designs

A class of Steiner 4-wise balanced designs derived from Preparata codes

The minimum weight codewords in the Preparata code of length n = 4 m are utilized for the construction of an innnite family of Steiner S(4; f5; 6g; 4 m + 1) designs for any m 2. A t-wise balanced design with parameters t-(v; K;) is a pair (X; B) where X is a set of v points and B is a collection of subsets of X (called blocks) with sizes from the set K, such that every t-subset of X is containe...

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.

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∗),...

Orthogonal arrays of strength three from regular 3 - wise balanced designsCharles

The construction given in 4] is extended to obtain new innnite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction.

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