Combinatorial Properties of Group Divisible Incomplete Block Designs

Bose, R. C.; Connor, W. S.

doi:10.1214/aoms/1177729382

Cited by 195 publications

(176 citation statements)

References 5 publications

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“…5 and 6 in [BC52]) For the number of elements of a generalized 2-(n, k, λ) design Y of type 3 one has |Y | ≥ 3n, for k < n, 2n + 1, for k = n. The set of the 45 weight 4 vectors in the Hexacode has the smallest cardinality for a generalized 2 − (6, 4, λ) design.…”

Section: Theorem 19mentioning

confidence: 99%

Self-dual codes over the Kleinian four group

Höhn

2003

Mathematische Annalen

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Section: Theorem 19mentioning

confidence: 99%

Self-dual codes over the Kleinian four group

Höhn

2003

Mathematische Annalen

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“…We shall use group divisible (GD) designs for constructing the solution of these designs . For the combinatorial properties and the methods of construction for these designs r~fer to Bose and Connor [3] and Bose, Shrikhande, and Bhattacharya [6]. Given vo = mono objects divided into mo groups each with no treatments, a GD design with parameters (14.5) is an arrangement of the objects in b o blocks each of size k o , such that any two objects belonging to the same group occur together in A 10 blocks, and any two objects belonging to different groups occur together in A20 blocks.…”

Section: Designs Belonging To Thementioning

confidence: 99%

The bridge tournament problem and calibration designs for comparing pairs of objects

Bose¹,

Cameron²

1965

J. RES. NATL. BUR. STAN. SECT. B. MATH. MATH. PHYS.

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The c lassical tournam e nt problem caiJ s for arranging v individuals int o tea ms o f /) p layers so that a pla yer is teamed th e sa m e number of times with each of th e other pla ye rs and a lso that eac h player is pitted eq ually often aga in st each of th e other players. The play of th e tuurn a m en t resu lt s in th e determination of difference in p e rformance of th e various pairings of th e g roups. In th e s pecial case when p = 2 each team co n s ist s of two players and th e d es igri s are call e d brid ge tourn a me nt designs .In high prec is iun ca libration one ca n m eas ure only the difference be tw ee n t wo nominally eq ual g ro up s S(l that if u objects a re to be int e rco mpare d in groups of fJ objects, th en th e so lution s tu th e to urnam e nt probl e m provid e sc hedul es for th e gl'll uping. Th ese des ig ns are useful in we ig hing a nd any o th e r m eas ul'e m c nt s where th e obj ec ts tu b e meas ure d ca n b e co mbin ed intu gl'll ups without loss of prec is ion or acc uracy ill th e compari sons.Tili s pape r pre se nt s ge ne ral m e thud s fill' co nstru c tin g of brid ge lourn a m e nt d es ign s, i. e ., for Lh t' case wh c n p = 2, fur all /1 ~ 50.Key Wurd s : Ca libration , ca li bration designs. co mbin a tori a l analysis , diffe re nce se ts, e xpe riment d es ig ns' , in c omplete bloc k d es igns, tournam e nt s , weighing de s ign s.

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“…The first portion of the theorem follows from known results on group divisible designs [2]. But we keep the discussion self-contained.…”

Section: Introductionmentioning

confidence: 99%