Existence of 4-GDDs with at most 50 points and 4-GDDs of types 6 3 and 9 3
| Autor: | Yudhistira A. Bunjamin, R. Julian R. Abel, Diana Combe |
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| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Group (mathematics) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Theoretical Computer Science Combinatorics Range (mathematics) 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Finite set Mathematics |
| Zdroj: | Discrete Mathematics. 344:112479 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2021.112479 |
| Popis: | In this paper we give two new refinements to the known necessary conditions for the existence of a 4-GDD and list all the feasible group types for 4-GDDs where the number of points v satisfies 31 ≤ v ≤ 50 . For v in this range, we obtain solutions for all feasible group types when v ≡ 0 ( mod 3 ) , and solutions for all feasible types of the form 4 s 1 t w 1 except 4 8 1 1 10 1 . We also obtain various other 4-GDDs. These include solutions for 4-GDDs of types 6 s 3 t and 9 s 3 t for all but a finite number of feasible values of s and t. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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