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From: bm373592@muenchen.org (Uenal Mutlu)
Newsgroups: sci.math,aus.mathematics,de.sci.mathematik,sci.math.num-analysis,sci.math.research
Subject: ANN: Some New Results in the Field of Discrete Math/Designs/Codes
Date: Wed, 27 Nov 1996 06:24:25 GMT
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Xref: lrz-muenchen.de sci.math:151945 aus.mathematics:542 de.sci.mathematik:2566 sci.math.num-analysis:28672 sci.math.research:6785

SOME NEW RESULTS IN THE FIELD OF DISCRETE MATH/DESIGNS/CODES

Date  : 96/11/27 We
Author: Uenal Mutlu (bm373592@muenchen.org)

The following bounds of enumerated 'm=t COVERING DESIGNS' are to
the best of my knowledge *NEW* upper bound results compared to
known published or online available results (cf. [1],[2],[4]).

Definition:

 A Covering Design C(v,k,t,m,l,b) is a pair (V,B), where V is a set
 of v elements (called points) and B is a collection of b k-subsets
 of V (called blocks), such that every m-subset of V intersects at
 least l members of B in at least t points (v >= k >= t and m >= t).


New upper bounds for C(v,k,t,m,l=1,b). Listed are m=t designs only:

 k t m	v     b (bOld)	Remarks/Author/Method
------------------------------------------------------------------
 6 4 4 15   118 (120)	Rade Belic, [3]
 6 5 5 14   377 (378)	Rade Belic, [3]
 6 5 5 15   609 (610)	Combine-Construction [1]
 7 5 5 17   408 (463)	Rade Belic, [3]
 7 5 5 18   618 (663)	Combine-Construction [1]
 7 5 5 19   772 (824)	Turan Theory/Sidorenko Construction [1]
 7 5 5 20  1115 (1153)	Combine-Construction [1]
 7 5 5 21  1424 (1476)	[3]
 7 5 5 22  1938 (1990)	[3]
 7 5 5 23  2405 (2458)	[3]
 7 5 5 24  3096 (3208)	[3]
 7 5 5 25  3772 (3830)	[3]

(bOld refers to the upper bounds of [2] on 96/11/26)

The new upper bounds were obtained by some published (see [1]) and
some not yet published algorithms and programs of Rade Belic [3]
and Uenal Mutlu (including implementations of some recursive
constructions from [1]).

These results will also improve some other designs with higher
k,t,m if at least some of the well known recursive construction
methods are applied.

Not shown are the latest improvements and new upper bounds for
designs with m > t. A list containing all upper bounds of enumerated
designs in the range k <= 7, v <= 54, t <= 7, m <= 7 and b <= 9999
can be requested from the author [5]).

Pointers to further improvements and new results are welcome.

Uenal Mutlu


References:

[1] D.M.Gordon, O.Patashnik, G.Kuperberg "New Constructions for
    Covering Designs", J.Combin.Designs 3.4 (1995) 269-284
    (for updates and errata see [2])

[2] Dan Gordon's "La Jolla Covering Repository" at
    http://sdcc12.ucsd.edu/~xm3dg/cover.html
    (as of 96/11/26)

[3] SOPT v1.0 07/96 (96/11/19) - Design Optimization Program
    written by Rade Belic

[4] D.R.Stinson "Coverings" in C.J.Colbourn, J.H.Dinitz (eds.)
    "The CRC Handbook of Combinatorics" CRC Press (1996) 260-265

[5] Uenal Mutlu "List of Covering Designs" (enumerated upper bounds)
    Includes also m > t designs. Current list is LST1127A.ZIP


-- Uenal Mutlu (bm373592@muenchen.org)   <http://www.tuco.com/math1.htm>
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany


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From: bm373592@muenchen.org (Uenal Mutlu)
Newsgroups: sci.math.research,sci.math
Subject: Re: ANN: Some New Results in the Field of Discrete Math/Designs/Codes
Date: Tue, 03 Dec 1996 02:27:24 GMT
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Approved: Daniel Grayson <dan@math.uiuc.edu>, moderator for sci.math.research
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Xref: lrz-muenchen.de sci.math.research:6859 sci.math:152630

On Wed, 27 Nov 1996 06:24:25 GMT, bm373592@muenchen.org (Uenal Mutlu) wrote:

>SOME NEW RESULTS IN THE FIELD OF DISCRETE MATH/DESIGNS/CODES
>
>Date  : 96/11/27 We
>Author: Uenal Mutlu (bm373592@muenchen.org)
>
>The following bounds of enumerated 'm=t COVERING DESIGNS' are to
>the best of my knowledge *NEW* upper bound results compared to
>known published or online available results (cf. [1],[2],[4]).
>
>Definition:
>
> A Covering Design C(v,k,t,m,l,b) is a pair (V,B), where V is a set
> of v elements (called points) and B is a collection of b k-subsets
> of V (called blocks), such that every m-subset of V intersects at
> least l members of B in at least t points (v >= k >= t and m >= t).
>
>
>New upper bounds for C(v,k,t,m,l=1,b). Listed are m=t designs only:
>
> k t m	v     b (bOld)	Remarks/Author/Method
>------------------------------------------------------------------
> 6 4 4 15   118 (120)	Rade Belic, [3]
> 6 5 5 14   377 (378)	Rade Belic, [3]
> 6 5 5 15   609 (610)	Combine-Construction [1]
> 7 5 5 17   408 (463)	Rade Belic, [3]
> 7 5 5 18   618 (663)	Combine-Construction [1]
> 7 5 5 19   772 (824)	Turan Theory/Sidorenko Construction [1]
> 7 5 5 20  1115 (1153)	Combine-Construction [1]
> 7 5 5 21  1424 (1476)	[3]
> 7 5 5 22  1938 (1990)	[3]
> 7 5 5 23  2405 (2458)	[3]
> 7 5 5 24  3096 (3208)	[3]
> 7 5 5 25  3772 (3830)	[3]

Here are some more new results/improvements:
  
  6 5 5 19  2210 (2211)      Turan Theory/Sidorenko Construction   
  7 5 5 14   143 (144)       I.Bluskov
  7 5 5 24  3094 (3096 s.a.) [3] 
  7 6 6 15   853 (854)       Rade Belic, [3] 
  7 6 6 16  1450 (1458)      [3]
  7 6 6 17  2165 (2167)      [3] 
  7 6 6 18  3392 (3394)      [3]


-- Uenal Mutlu (bm373592@muenchen.org)   <http://www.tuco.com/math1.htm>
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany


