(M, S)-optimal designs with block size three

نویسندگان

  • Charles J. Colbourn
  • Alan C. H. Ling
چکیده

The existence of (M, B)-optimal designs for block size three is completely settled. Such a design is a collection of b triples on v elements so that for every two elements the numbers of triples containing them differ by at most one, and for every two pairs of elements the numbers of triples containing them also differ by at most one.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Some Optimal Codes From Designs

The binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. A new method is also introduced to study optimal codes.

متن کامل

Optimal 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 کامل

Some E-optimal Designs for cDNA Microarray Experiments

In this paper, optimal incomplete block designs were determined for cDNA microarray experiments, where arrays are blocks, block size is always two, and the number of blocks or arrays available is approximately equal to the number of samples. A new class of designs, the mixed designs, which are a mixture of reference and loop designs, have been identified and their optimality has been proven in ...

متن کامل

A Family of Group Divisible Designs of Block Size Four and Three Groups With l1=2 and l2=1 Using MOLS

We give a construction for a new family of Group Divisible Designs (6s+ 2, 3, 4; 1, 2) using Mutually Orthogonal Latin Squares for all positive integers s. Consequently, we have proved that the necessary conditions are sufficient for the existence of GDD’s of block size four with three groups, λ1=2 and λ2=1.

متن کامل

Block designs for symmetric parallel line assays with block size odd

SUMMARY. In a parallel line assay, there are three treatment contrasts of major importance. Block designs allowing the estimability of all the three contrasts free from block effects, called L-designs, necessarily have the block sizes even. For odd block sizes, we provide here a class of highly efficient designs, called nearly L-designs. These nearly L-designs have been constructed by establish...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Australasian J. Combinatorics

دوره 23  شماره 

صفحات  -

تاریخ انتشار 2001