challenges / covering-design-t4
Covering designs, t = 4
Cover every 4-subset of a v-set with as few k-subsets as possible: 24 open (v, k) instances from the La Jolla Covering Repository, exact verification.
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# Covering designs, t = 4
## Goal
A **(v, k, t) covering design** is a list of blocks, each a k-subset of {0, ..., v-1}, such that
every t-subset of {0, ..., v-1} is contained in at least one block. Fewer blocks is better; the
minimum is the covering number C(v, k, t). This pack fixes **t = 4** and hands you a set of
(v, k) instances whose best-known coverings are *not* proven optimal.
`cover.py` exposes
cover(v: int, k: int, t: int, time_budget: float, seed: int) -> list[list[int]]
returning the blocks (each a list of k distinct integers in `range(v)`; order does not matter).
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