In block design, construction of Balanced Incomplete Block Design (BIBD) remained an unsolved problem in combinatorial design; also various techniques have been introduced to build the elements BIBDs for specific parameters; no general method has proposed find a suitable structure BIBDs. This paper aim at employing Finite Euclidean Geometry FEG (N,s) N – dimensional space construct balan...

A balanced incomplete block design BIBD(v, k, λ) is a pair (V,B) where V is a v-set (points) and B is a collection of k-subsets of V (blocks) such that each pair of elements of V occurs in exactly λ blocks. A k-tournament is a directed graph on k vertices in which there is exactly one arc between any two distinct vertices. Given a k-tournament T , we call a BIBD(v, k, 2) T -orientable if it is ...

We say that an A 2-code is optimum if it has the minimum cheating probabilities and the minimum sizes of keys. We rst show that an optimum A 2-code implies an aane-resolvable design. Next, we de-ne an aane-resolvable + BIBD design and prove that an optimum A 2-code is equivalent to an aane-resolvable + BIBD design.

A decomposition of λ copies of monochromatic Kv into copies of K4 such that each copy of K4 contains at most one edge from each Kv is called a proper edge coloring of a BIBD(v, 4, λ). We show that the necessary conditions are sufficient for the existence of a BIBD(v, 4, λ) which has such a proper edge coloring.

A (v, m, m − 1)-BIBD D is said to be near resolvable (NRBIBD) if the blocks of D can be partitioned into classes R1, R2, . . . , Rv such that for each point x of D, there is precisely one class having no block containing x and each class contains precisely v − 1 points of the design. If an (v, m, λ)-NRBIBD has a pair of orthogonal resolutions, it is said to be doubly resolvable and is denoted D...

BACKGROUND Multiple neurodegenerative diseases are characterized by the abnormal accumulation of FUS protein including various subtypes of frontotemporal lobar degeneration with FUS inclusions (FTLD-FUS). These subtypes include atypical frontotemporal lobar degeneration with ubiquitin-positive inclusions (aFTLD-U), basophilic inclusion body disease (BIBD) and neuronal intermediate filament incl...

Symmetric Balanced Incomplete Block Designs with λ=1 is a common class of BIBDs which are mostly used in incomplete experimental block design set up because their simplicity and also analysis. Over the years since development by Yates year 1939. A number research has been done on to establish properties determine construction methods design. In terms properties, studies have only able necessary...