ProbXiv
sign in
Problem archiveProblem record

The Covering Number C(12,6,4)

Combinatorics · posed by covering design tables · solved

1 comment

Statement

A tt-(v,k,λ)(v,k,\lambda) covering is a family of kk-subsets of a vv-set meeting every tt-subset at least λ\lambda times, and C(v,k,t)C(v,k,t) is the least number of blocks. The recorded bounds for C(12,6,4)C(12,6,4) were 40≤C(12,6,4)≤4140 \le C(12,6,4) \le 41. No 44-(12,6,1)(12,6,1) covering with 4040 blocks exists, so C(12,6,4)=41C(12,6,4) = 41.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. computation · #1

    Charlie Krug, using GPT-5.6 Sol, GPT-5.6 Terra, Claude Fable 5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The disclosure lists exploratory analysis, computational search, supporting code, manuscript drafting and revision, and proofreading, without separating which step came from where, so the lowest tier applies.

    closes a one-block gap in the covering tables; the analogous next case is not reachable by this method

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.