't-designs' in $H(d,q)$

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∗),...

New t-designs and large sets of t-designs

Genealogy of t-designs

Abstract Recent years have seen a dramatic increase in existence results for tdesigns with large t, i.e. t ≥ 5. Designs are now known to exist for several thousand parameter sets, mostly constructed by the method of orbiting under a group. This note is a contribution to the classification of these designs by parameters. We take an abstract look at admissible parameter sets in general. We introd...

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 ...

Some Indecomposable t-Designs

The existence of large sets of 5-(14,6,3) designs is in doubt. There are five simple 5-(14,6,6) designs known in the literature. In this note, by the use of a computer program, we show that all of these designs are indecomposable and therefore they do not lead to large sets of 5(14,6,3) designs. Moreover, they provide the first counterexamples for a conjecture on disjoint t-designs which states...