Plain language

What this result means

Covering arrays are compact test suites: every t-way interaction still appears, but fewer rows means fewer tests. This result matters because it separates a promised size from a built object. The array has to exist before it can be a record.

  • CA(N;t,k,v) means N rows, k columns, and v symbols. For every choice of t columns, all v^t tuples must appear somewhere.
  • The largest margins come from ordered-design constructions; most of the individual cells come from Torres-Jimenez binary arrays.
  • Some attractive size predictions were rejected because they did not build at the claimed size. The kept rows are actual arrays.

Visual notes

How to read the result

Horizontal bar chart of the largest covering-array row savings.
Rows savedThe ordered-design rows create the largest margins; the full run contains 40 table improvements.
Two stacked bar charts showing rows saved and arrays found by construction source.
Where the savings came fromOrdered design accounts for most rows saved, while Torres-Jimenez accounts for most individual cells.
Barcode-like rendering of the actual binary covering array with 143 rows and 199 columns.
One actual witnessThis is the stored CA(143;4,199,2) binary array rendered as a barcode, not a schematic.

Result table

Forty explicit arrays lowered Colbourn table values.

CellBaselineNumaroDeltaNote
CA(14928;3,8,24)15,18014,928-252 rowsordered design
CA(8760;3,8,20)8,9308,760-170 rowsordered design
CA(9330;3,12,20)9,5009,330-170 rowsordered design
CA(6444;3,8,18)6,5796,444-135 rowsordered design
CA(143;4,199,2)154143-11 rowsTorres-Jimenez
CA(2215;3,16,10)2,2232,215-8 rowsCK doubling
CA(421;6,29,2)426421-5 rowsTorres-Jimenez
CA(2615;3,41,10)2,6182,615-3 rowsDwyer database

Method

How it was found

The campaign compared listed CAN values against arrays obtainable from standard construction catalogues, then built the candidates and kept only arrays that actually checked out.

  • Triple-confirmed the Colbourn baseline values from the mirror and CAs package data.
  • Used construction catalogues to propose smaller N values.
  • Materialized each candidate as an explicit array; predictions that failed to build at the claimed size were dropped.
  • Checked every kept array against every column-subset and tuple requirement.

Verification

How it was checked

For each array, the checker reads the N x k table, checks that every entry is in the allowed symbol range, then tries every choice of t columns and confirms that all v^t tuples appear. All 40 kept arrays pass with zero missing requirements.

Scope

What is not being claimed

These are best-known improvements, not optimality proofs. The underlying arrays come from published constructions and catalogues. The contribution is detecting the table-beating cells, building the objects, and checking them from scratch.

References

Baseline sources

Citation

How to cite

Numaro Autoresearch Team. "Covering-array records improving Colbourn's best-known CAN tables." Numaro Research Report NUMARO-2026-007, 2026.

@techreport{numaro2026CoveringArraysColbourn,
  title = {Covering-array records improving Colbourn's best-known CAN tables},
  author = {Numaro Autoresearch Team},
  institution = {Numaro},
  number = {NUMARO-2026-007},
  year = {2026},
  url = {https://numaro.tech/research/covering-arrays-colbourn-2026/}
}