Nonexistence of a few binary orthogonal arrays

Nonexistence of certain binary orthogonal arrays

We prove that binary orthogonal arrays of strength 8, length 12 and cardinality 1536 do not exist. This implies the nonexistence of arrays of parameters (strength,length,cardinality) = (n, n + 4, 6.2) for every integer n ≥ 8.

Nonexistence of (9, 112, 4) and (10, 224, 5) binary orthogonal arrays

Nonexistence of ( 9 , 112 , 4 ) and ( 10 , 224 , 5 ) binary orthogonal arrays 1

Our approach is a natural continuation of the algorithm which is presented in [3]. We prove the nonexistence of BOAs of parameters (length, cardinality, strength) = (9, 7.2 = 112, 4) and (10, 7.2 = 224, 5), resolving two cases where the existence was undecided up to now.

On the existence of nested orthogonal arrays

A nested orthogonal array is an OA(N, k, s, g)which contains an OA(M, k, r, g) as a subarray. Here r < s andM<N . Necessary conditions for the existence of such arrays are obtained in the form of upper bounds on k, given N,M, s, r and g. Examples are given to show that these bounds are quite powerful in proving nonexistence. The link with incomplete orthogonal arrays is also indicated. © 2007 E...

β-galactosidase Production by Aspergillus niger ATCC 9142 Using Inexpensive Substrates in Solid-State Fermentation: Optimization by Orthogonal Arrays Design

Background: Enzymatic hydrolysis of lactose is one of the most important biotechnological processes in the food industry, which is accomplished by enzyme &beta;-galactosidase (&beta;-gal, &beta;-D-galactoside galactohydrolase, EC 3.2.1.23), trivial called lactase. Orthogonal arrays design is an appropriate option for the optimization of biotechnological processes for the production of microbial...