The fundamental construction for 3-designs
Proceedings of the first Malta conference on Graphs and combinatorics
The last packing number of quadruples, and cyclic SQS
Designs, Codes and Cryptography
New constant-weight codes from propagation rules
IEEE Transactions on Information Theory
List decodability at small radii
Designs, Codes and Cryptography
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A 3-(n,4,1) packing design consists of an n-element set X and a collection of 4-element subsets of X, called blocks, such that every 3-element subset of X is contained in at most one block. The packing number of quadruples d(3,4,n) denotes the number of blocks in a maximum 3-(n,4,1) packing design, which is also the maximum number A(n,4,4) of codewords in a code of length n, constant weight 4, and minimum Hamming distance 4. In this paper the last packing number A(n,4,4) for n驴 5(mod 6) is shown to be equal to Johnson bound $J(n,4,4)(=\lfloor\frac{n}{4}\lfloor\frac{n-1}{3}\lfloor\frac{n-2}{2}\rfloor\rfloor\rfloor)$ with 21 undecided values n=6k+5, k驴{m: m is odd , 3驴 m驴 35, m驴 17,21}驴 {45,47,75,77,79,159}.