An embedding theorem for affine resolvable designs
نویسندگان
چکیده
منابع مشابه
Rigidity Theorems for a Class of Affine Resolvable Designs
The affine resolvable 2-(27, 9, 4) designs were classified by Lam and Tonchev [9, 10]. We use their construction of the designs to examine the ternary codes of the designs and show, using Magma [3], that each of the codes, apart from two, contains, amongst its constant weight-9 codewords, a copy of the ternary code of the affine geometry design of points and planes in AG3(F3). We also show how ...
متن کاملThickly-resolvable block designs
We show that the necessary divisibility conditions for the existence of a σ-resolvable BIBD(v, k, λ) are sufficient for large v. The key idea is to form an auxiliary graph based on an [r, k]-configuration with r = σ, and then edge-decompose the complete λ-fold graph K (λ) v into this graph. As a consequence, we initiate a similar existence theory for incomplete designs with index λ. ∗ Supported...
متن کاملSome Block Designs Constructed from Resolvable Designs
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, ...
متن کاملResolvable Designs with Large Blocks
Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix, and consequently in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Su...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90125-x