Some Block Designs Constructed from Resolvable Designs
نویسنده
چکیده
LetD be a resolvable 2−(v, k, λ) design, andD′ be a 2−(v′, k′, λ′) design, such that v′ = v k . Further, let r and r′ be replication numbers of a point in D and D′, respectively. Shrikhande and Raghavarao proved that then there exists a 2 − (v′′, k′′, λ′′) design D′′, such that v′′ = v, k′′ = kk′ and λ′′ = r′λ + (r − λ)λ′. If D′ is resolvable, then D′′ is also resolvable. Applying this result, we construct block designs from some series of designs. Further, we discuss a construction of resolvable 3-designs.
منابع مشابه
Difference families with applications to resolvable designs
Some block disjoint difference families are constructed in rings with the property that there are k distinct units uit 0 < i < k — 1, such that differences ut — Uj (0 < i < j < k — 1) are all units. These constructions are utilized to produce a large number of classes of resolvable block designs.
متن کاملUniformly resolvable designs with index one and block sizes three and four - with three or five parallel classes of block size four
Each parallel class of a uniformly resolvable design (URD) contains blocks of only one block size. AURDwith v points andwith block sizes three and fourmeans that at least one parallel class has block size three and at least one has block size four. Danziger [P. Danziger, Uniform restricted resolvable designs with r = 3, ARS Combin. 46 (1997) 161–176] proved that for all v ≡ 12 (mod 24) there ex...
متن کاملA new look at an old construction: Constructing (simple) 3-designs from resolvable 2-designs
In 1963, Shrikhande and Raghavarao [5] published a recursive construction for designs that starts with a resolvable design (the “master design”) and then uses a second design (“the indexing design”) to take certain unions of blocks in each parallel class of the master design. Several variations of this construction have been studied by different authors. We revisit this construction, concentrat...
متن کاملOptimal resolvable designs with minimum PV aberration
Amongst resolvable incomplete block designs, affine resolvable designs are optimal in many conventional senses. However, different affine resolvable designs for the same numbers of treatments, replicates, and block size can differ in how well they estimate elementary treatment contrasts. An aberration criterion is employed to distinguish the best of the affine resolvable designs for this task. ...
متن کاملClass-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs
We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master de...
متن کامل