2025/08/18 by Etzion, Tuvi · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.12954
We prove that a 3-GDD of type 1n k1 ℓ1, where n= k ⋅ ℓ, with minimum distance 3 exists for every k and ℓ such that n = k ℓ, k = 1 or 3~(mod ~ 6), and ℓ = 1 or 3~(mod ~ 6). These designs are of the shortest possible length (smallest number of elements) for given k and ℓ. Other constructions for such triple systems are also presented.