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What is a Covering Design?

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. It is required that v >= k >= t and m >= t. The case m > k is also a valid case. B can be a multiset.

bulletDN - What's a Wheel



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  bulletLa Jolla Covering Repository

The site contains coverings C(v,k,t) with v<=32, k<=16, t<=8, and less than 5,000 blocks.

bulletPeter's Wheels

Collection of wheels, k<=10, Peter Rosendahl.

bulletRade Belic Repository

bulletDesign  C( 49, 6, 3, 6, 1, 168, p=100%) 

Uenal Mutlu's covering design that guarantees min. 3 numbers on a 49c6 Lotto

bulletDesign  C( 49, 6, 2, 6, 1, 19, p=100%)

Covering Design that guarantees 2 numbers on a 49c6 Lotto



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bulletBounds List  -  Rade Belic Repository

bulletImprovements List



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bulletDN - Search  -  Partial Covering Designs

bulletDN - Re Performance Index for Covering Designs Wheels

bulletDN - Re Partial Covering Designs Wheels



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bulletConstruction methods for covering codes   VW_abs.gif (1045 bytes)

bulletDesign Theory and Coding Theory   VW_abs.gif (1045 bytes)

bulletConstructing covering designs by simulated annealing   VW_abs.gif (1045 bytes)

bulletConstructing combinatorial designs by local search  VW_abs.gif (1045 bytes)

bulletConstructions of mixed covering codes  VW_abs.gif (1045 bytes)

bulletConstructing spherical codes by global optimization methods  VW_abs.gif (1045 bytes)

bulletNew upper bounds for binary/ternary mixed covering codes VW_abs.gif (1045 bytes)

bullet``Completely regular designs.''    VW_ps.gif (1078 bytes)

bullet``Mixed block designs.''    VW_ps.gif (1078 bytes)

bulletComplete Arcs in Steiner Triple Systems   VW_dvi.gif (1033 bytes)


bulletIntroduction to Global Optimization 

bulletMy Views on Some Global Optimization Methods

bulletYahoo! - Science Mathematics Combinatorics

bulletResouces - Simulated Annealing Information


bulletHandbook of Combinatorial Desgns

Book, Combinatorics.

bulletMathematics Archives WWW Server

Select mathematics field of your interest

bulletGateway to Mathematics

bulletAn entirely different sort of Game Theory

bulletGame Theory Resources on the Net


For more informations visit our Combinatorics page.  Click here

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(125 KB) v1.31+ Author U.Mutlu, Commandline Pgm for Win95/NT

(67 KB) v1.20+ Author R.K.Lloyd, includes C-Source, multiple platforms



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Research paper and program for covering designs (C-Source for 32-bit compilers)


t-designs and algebra system, public domain software


t-designs and algebra system

bulletPhilippe Coustaux - PCLoto

bulletUse DOPT to find good incomplete-block designs for fitting 



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bulletThe WWW  Virtual Library Random Numbers & Monte Carlo methods

bulletYahoo! - Science ,   Mathematics ,  Numbers ,  Random Numbers

bulletNumber Generators

bulletGames - Lotto Number Generators

bulletResources - Random Number Generation


bulletPick Your Lottery Number's HERE! Javascript number picker

bulletLottery number selector page

bulletLoterie Romande Swiss Lotto Random Number Generator



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bulletSnippets of C code

bulletImproved Snub Cube and Other New Spherical Designs in Three  VW_ps.gif (1078 bytes)

bulletCombinatoric algorithms



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bulletDN - Insurance Wheel

bulletWheel Analysis - a report

bulletLattices & t-designs

bulletNew Construction for Covering Designs  VW_abs.gif (1045 bytes)

bulletTwo Series of BIB Designs



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bulletDN - Probability Wheels and Strategy

bulletDN - Re wanted algorithm for reducing #of lines

bulletDN - Re Covering Space Crieria


bulletDN - Search  - Wheeling Algorithm

bulletDN - Partial Covering Designs

bulletDN - Re Wheeling Algorithm Thoughts

bulletDN - Re 174 Ticket Challenge

bulletDN - The Worse Possible Sets

bulletDN - Probability and Wheels

bulletDN - Subject: 27 Tickets

bulletDN - Subject: 7 Number

bulletDN - Repost #1 - How Wheels CAN save you money


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C  = Covering Design, Wheel
v   = total numbers (ie. 49)
k   = numbers per ticket (ie. 6)
t    = minimum hit size (ie. 2)
m  = if within the v-(total numbers) have maximum hits (ie. 6)
l    = guarantees how many times t-minimum hits will occur within the design (ie. 1)
b   = number of tickets (>= 1) 

Example 1: C(31,6,2,2,1,31)
=  A wheel(with 31 nbr,6 nbr per ticket, minimum hits 2, if within total numbers have 2 hits, quantity of 2 hits =1, with 31 tickets )

Example 2: C(49,6,3,6,1,168)
= A wheel(with 49 nbr,6 nbr per ticket, minimum hits 3, if within total numbers have 6 hits, quantity of 3 hits =1, with 168 tickets )

For more information see our Glossary page. Click here


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