Table for CAN(5,k,13) for k up to 10000

Last Updated Tue Mar 8 20:11:31 MST 2022

Locate the k in the first column that is at least as large as the number of factors in which you are interested. Then let N be the number of rows (tests) given in the second column. A CA(N;5,k,13) exists according to a construction in the reference (cryptically) given in the third column. The accompanying graph plots N vertically against log k (base 10).

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kNSource
14371293orthogonal array
15711828extended OA (Colbourn)
167140254-Restricted SCPHF RE (CL)
187403893-Restricted SCPHF RE (CL)
19742573SCPHF Random Extension (CLS)
2910853054-Restricted SCPHF RE (CL)
3111116693-Restricted SCPHF RE (CL)
331113877CPHF IPO 3 (WCS)
4414280374,4-Restricted SCPHF RE (CL)
4714544014,3-restricted SCPHF RE (CL)
4814565854-Restricted SCPHF RE (CL)
5114807653,3-Restricted SCPHF RE (CL)
5214827933,2-restricted SCPHF RE (CL)
5314829493-Restricted SCPHF RE (CL)
5514849772-Restricted SCPHF RE (CL)
621485169CPHF IPO 4 (WCS)
7517993174,4-Restricted SCPHF RE (CL)
8418278654-Restricted SCPHF RE (CL)
8818542293-Restricted SCPHF RE (CL)
9218562572-Restricted SCPHF RE (CL)
931856413SCPHF Random Extension (CLS)
1111856461CPHF IPO 5 (WCS)
12021705974,4-Restricted SCPHF RE (CL)
14021991454-Restricted SCPHF RE (CL)
15322255093-Restricted SCPHF RE (CL)
15622275372-Restricted SCPHF RE (CL)
1572227693SCPHF Random Extension (CLS)
1882227753CPHF IPO 6 (WCS)
20925418774,4-Restricted SCPHF RE (CL)
23725704254-Restricted SCPHF RE (CL)
26125967893-Restricted SCPHF RE (CL)
27125988172-Restricted SCPHF RE (CL)
2722598973SCPHF Random Extension (CLS)
32428846094,4,4-Restricted SCPHF RE (CL)
34929131574,4-Restricted SCPHF RE (CL)
37929417054-Restricted SCPHF RE (CL)
44229680693-Restricted SCPHF RE (CL)
45029700972-Restricted SCPHF RE (CL)
4522970253SCPHF Random Extension (CLS)
4542970337CPHF Random Extension (CLS)
52332558894,4,4-Restricted SCPHF RE (CL)
56732844374,4-Restricted SCPHF RE (CL)
65333129854-Restricted SCPHF RE (CL)
75033393493-Restricted SCPHF RE (CL)
76433413772-Restricted SCPHF RE (CL)
7673341533SCPHF Random Extension (CLS)
7684706377Add 1 factors
7695681845Add 2 factors
7706024577Add 3 factors
7776367153Add 13 factors
7806367309Add 13 factors
7817732153Add 13 factors
7828707621Add 13 factors
7839050353Add 13 factors
7869392929Add 13 factors
7889394801Add 13 factors
7899396673Add 13 factors
7909398545Add 13 factors
7939398701Add 13 factors
8159646764perfect hash family3,1122,749T307
8239648792perfect hash family3,1122,749T299
8259648948perfect hash family3,1122,749T297
8279649032perfect hash family3,1122,749T295
8309652848perfect hash family3,1143,763T313
8329653004perfect hash family3,1143,763T311
8349653088perfect hash family3,1143,763T309
8369653400perfect hash family3,1149,767T313
8499853308perfect hash family3,849,567
8929910404perfect hash family3,978,653T86
8969934584perfect hash family3,1122,749T226
9039938640perfect hash family3,1143,763T240
9789938952perfect hash family3,978,653
10269991680perfect hash family3,1122,749T96
10339995736perfect hash family3,1143,763T110
10359996048perfect hash family3,1149,767T114
112310018044perfect hash family3,1123,750
113010022100perfect hash family3,1143,763T13
113210022412perfect hash family3,1149,767T17
114410024128perfect hash family3,1144,764
114610024440perfect hash family3,1149,767T3
114910024596perfect hash family3,1149,767
115011632800Add 1 factors
118512509376perfect hash family4,3125,625T388
124712509592Power N-CT43^2T14
130512535740perfect hash family4,3125,625T364
133312535956Power N-CT43^2T12
135512537768perfect hash family4,3125,625T354
136012537924perfect hash family4,3125,625T353
141912538164Power N-CT43^2T10
145212722712Power N-CT47^2T14T3
145712746868Power N-CT47^2T16
155112749076Power N-CT47^2T14
162012823560perfect hash family4,3125,625T301
174512852108perfect hash family4,3125,625T276
185012852324Power N-CT43^2+1
189512880656perfect hash family4,3125,625T246
221012907020perfect hash family4,3125,625T183
225012909048perfect hash family4,3125,625T175
226012909204perfect hash family4,3125,625T173
227012909288perfect hash family4,3125,625T171
261513194840perfect hash family4,3125,625T102
283513223388perfect hash family4,3125,625T58
312513251936perfect hash family4,3125,625
317213364136Power N-CT61^2T9
323313364292Power N-CT61^2T8
335513366320Power N-CT61^2T6
372213366512Power N-CT61^2+1
372315315420Add 1 factors
384415565548Power N-CT67^2T5T5
386915877476Power N-CT73^2T20
401515879504Power N-CT73^2T18
452615879696Power N-CT73^2T11
465016079532Power N-CT79^2T17T4
514616108080Power N-CT83^2T21
533116193844Power N-CT73^2+2
533516329132Power N-CT89^2Arc(3)T27
539516331160Power N-CT89^2Arc(2)T27
555916332444perfect hash family9,11881,109T58
566816334472perfect hash family9,11881,109T57
577716334628perfect hash family9,11881,109T56
599516336656perfect hash family9,11881,109T54
675816336848perfect hash family9,11881,109T47
689016450776Power N-CT83^2+1
697716647492Power N-CT89^2Trin1,5,5
705616649520Power N-CT89^2T5T5
817516650996perfect hash family9,11881,109T34
915616679544perfect hash family9,11881,109T25
959216705908perfect hash family9,11881,109T21
1000016707936perfect hash family9,11881,109T17
 Graph: