Plain language

What this result means

This result matters because the system treated the repository as a dependency graph, not just a list of numbers. A better source covering can imply a better derived covering. The record only counts after the derived object is actually built and checked.

  • A (v,k,t)-covering is a set of k-point blocks. Every t-point subset must appear inside at least one block; fewer blocks is better.
  • The four records come from the standard induction relation C(v,k,t) <= C(v-1,k-1,t-1) + C(v-1,k,t).
  • This is not a claim that the source coverings are new. The win is detecting the unpropagated derived cells, materializing the witnesses, and checking them.

Visual notes

How to read the result

Horizontal bar chart of four covering-design improvements measured in blocks saved.
Blocks savedThe largest row saves 4,160 blocks; all four rows are strictly below the listed La Jolla value.
Stacked bars showing source-covering counts that sum to each derived covering record.
The induction witnessEach derived covering is built from two source coverings through the standard R4 construction.
Log-scale chart comparing the number of subsets behind each covering-design row.
Checklist scaleThe t=4 row can be enumerated directly. The t=7 and t=8 rows are too large for brute-force enumeration here, so the proof goes through the theorem and the source coverings.

Result table

Four covering numbers lowered below the La Jolla table.

CellBaselineNumaroDeltaNote
C(77,25,8)179,223175,063-4,160R4 theorem (C(76,24,7) + C(76,25,8))
C(92,7,4)132,580131,122-1,458exhaustive: 2,794,155 subsets (C(91,6,3) + C(91,7,4))
C(86,23,7)153,683153,047-636R4 theorem (C(85,22,6) + C(85,23,7))
C(79,21,7)165,213165,027-186R4 theorem (C(78,20,6) + C(78,21,7))

Method

How it was found

The campaign parsed the LJCR table, propagated standard covering relations to a fixpoint, and kept the four cells where the current table lagged the induction construction.

  • Fetched and parsed 9,482 LJCR entries.
  • Applied delete-point, enlarge-block, reduce-t, and R4 induction relations.
  • Built each derived covering from the two linked LJCR source coverings.
  • Checked nearby mature cells with CP-SAT and simulated annealing; those attempts matched records but did not beat them.

Verification

How it was checked

Each candidate has to have the claimed number of blocks, the right block size, and points in the correct range. For C(92,7,4), every one of the 2,794,155 four-point subsets is checked directly. For the larger rows, the check rebuilds the two source counts and uses the standard induction theorem: subsets containing the new point are covered by one source; subsets not containing it are covered by the other.

Scope

What is not being claimed

These are best-known improvements, not optimality proofs. LJCR is a strong mature repository; the point here is a narrow propagation gap, not that the table is broadly weak. The underlying source coverings are not claimed as new.

References

Baseline sources

Citation

How to cite

Numaro Autoresearch Team. "Covering-design records improving the La Jolla Covering Repository." Numaro Research Report NUMARO-2026-006, 2026.

@techreport{numaro2026CoveringDesignsLa,
  title = {Covering-design records improving the La Jolla Covering Repository},
  author = {Numaro Autoresearch Team},
  institution = {Numaro},
  number = {NUMARO-2026-006},
  year = {2026},
  url = {https://numaro.tech/research/covering-designs-la-jolla-2026/}
}