Maximal arcs and group divisible designs

Maximal arcs and quasi-symmetric designs

In 2001, Blokhuis and Haemers gave an interesting construction for quasisymmetric designs with parameters 2-(q, q(q − 1)/2, q(q − q − 2)/4) and block intersection numbers q(q − 2)/4 and q(q − 1)/4 (where q ≥ 4 is a power of 2), which uses maximal arcs in the affine plane AG(2, q) and produces examples embedded into affine 3-space AG(3, q). We consider this construction in more detail and in a m...

Construction of Group Divisible Designs

Divisible designs with dual translation group

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space. AMS Classification: 05B05, 05B30, 20B25, 51N10

(3, Λ)-group Divisible Covering Designs

Let U, g, k and A be positive integers with u :::: k. A (k, A)-grOUp divisible covering design ((k, A)-GDCD) with type gU is a A-cover of pairs by k-tuples of a gu-set X with u holes of size g, which are disjoint and spanning. The covering number, C(k, A; gil), is the minimum number of blocks in a (k, A)-GDCD of type gUo In this paper, the detennination ofllie fimction C(3, A; gil) begun by [6]...

Resolvable Group Divisible Designs with Large Groups

We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete mult...