We complete the classification of tight 4-designs in Hamming association schemes H(n,q), i.e., that of tight orthogonal arrays of strength 4, which had been open since a result by Noda (1979). To do so, we construct an association scheme attached to a tight 4-design in H(n,q) and analyze its triple intersection numbers to conclude the non-existence in all open cases.
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Alexander L. Gavrilyuk is supported by BK21plus Center for Math Research and Education at Pusan National University, and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (grant number NRF-2018R1D1A1B07047427). Sho Suda is supported by JSPS KAKENHI Grant Number 18K03395. Janos Vidali is supported by the Slovenian Research Agency (research program Pl-0285 and project J1-8130).
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Gavrilyuk, A.L., Suda, S. & Vidali, J. On Tight 4-Designs in Hamming Association Schemes. Combinatorica 40, 345–362 (2020). https://doi.org/10.1007/s00493-019-4115-z
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