A linear

If we are prepared to accept codes whose dual minimum distance is three then this will answer the more general question for

Alternatively, the longest linear

If you know of any improvement to this table, then please e-mail the address below. I have not finished updating all the links but if there is a value in the table that you wish to know about then please e-mail the address below.

*** Amendment of the table December 2009 - First change in the table since April 2008 with the discovery of a (79,6)-arc in PG(2,17) and a (126,8)-arc in PG(2,19) by Axel Kohnert. Click on the links below for data. ***

*** Amendment of the table January 2010 - Rumen Daskalov and Elena Metodieva construct a (95,7)-arc and a (183,12)-arc in PG(2,17) and a (243,14)-arc and a (264,15)-arc in PG(2,19). Click on the links below for data. ***

*** Amendment of the table June 2010 - Aaron Gulliver constructs a (78,8)-arc in PG(2,11). Click on the link below for data. ***

*** Amendment of the table July 2011 - Axel Kohnert and Johannes Zwanzger construct a (265,15)-arc in PG(2,19). Click on the link below for data. ***

*** Amendment of the table July 2011 - Rumen Daskalov constructs a (286,16)-arc in PG(2,19). Click on the link below for data. ***

*** Amendment of the table January 2012 - Gary Cook proves that there are no (34,4)-arcs, nor (33,4)-arcs in PG(2,11). Click on the link below for data. ***

*** Amendment of the table November 2012 - Daniele Bartoli, Stefano Marcugini and Fernanda Pambianco prove that there are no (29,3)-arcs in PG(2,16). See this article published in

*** Amendment of the table April 2013 - Noboru Hamada, Tatsuya Maruta and Yusuke Oya prove that there are no (34,3)-arcs in PG(2,17). Click on the link below for the proof. ***

*** Amendment of the table September 2017 - Thanks to Rumen Daskalov who has provided examples for all the lower bounds in PG(2,13), PG(2,17) and PG(2,19). Click on the links below for the examples. ***

*** Observation: There have been no improvements on the values in the table for more than four years.

q r=n-d | 3 | 4 | 5 | 7 | 8 | 9 | 11 | 13 | 16 | 17 | 19 |
---|---|---|---|---|---|---|---|---|---|---|---|

2 |
4 | 6 | 6 | 8 | 10 | 10 | 12 | 14 | 18 | 18 | 20 |

3 |
9 | 11 | 15 | 15 | 17 | 21 | 23 | 28 | 28 ... 33 | 31 ... 39 | |

4 |
16 | 22 | 28 | 28 | 32 | 38 ... 40 | 52 | 48 ... 52 | 52 ... 58 | ||

5 |
29 | 33 | 37 | 43 ... 45 | 49 ... 53 | 65 | 61 ... 69 | 68 ... 77 | |||

6 |
36 | 42 | 48 | 56 | 64 ... 66 | 78... 82 | 79 ... 86 | 86 ... 96 | |||

7 |
49 | 55 | 67 | 79 | 93 ... 97 | 95 ... 103 | 105 ... 115 | ||||

8 |
65 | 78 | 92 | 120 | 114 ... 120 | 126 ... 134 | |||||

9 |
89 ... 90 | 105 | 129 ... 130 | 137 | 147 ... 153 | ||||||

10 |
100 ... 102 | 118 ... 119 | 142 ... 148 | 154 | 172 | ||||||

11 |
132 ... 133 | 159 ... 164 | 166 ... 171 | 191 | |||||||

12 |
145 ... 147 | 180 ... 181 | 183 ... 189 | 204 ... 210 | |||||||

13 |
195 ... 199 | 205 ... 207 | 225 ... 230 | ||||||||

14 |
210 ... 214 | 221 ... 225 | 243 ... 250 | ||||||||

15 |
231 | 239 ... 243 | 265 ... 270 | ||||||||

16 |
256 ... 261 | 286 ... 290 | |||||||||

17 |
305 ... 310 | ||||||||||

18 |
324 ... 330 |

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Simeon Ball

simeon@ma4.upc.edu

4 September 2017