The completion of optimal (3,4)(3,4)-packings

A 3-$(n,4,1)$ packing design consists of an $n$-element set $X$ and a collection of $4$-element subsets of $X$, called {\it 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 undecided 21 packing numbers $A(n,4,4)$ are shown to be equal to Johnson bound $J(n,4,4)$ $( =\lfloor\frac{n}{4}\lfloor\frac{n-1}{3}\lfloor\frac{n-2}{2}\rfloor\rfloor\rfloor)$ where $n=6k+5$, $k\in \{m:\ m$ is odd, $3\leq m\leq 35,\ m\neq 17,21\}\cup \{45,47,75,77,79,159\}$

Large sets of extended directed triple systems with even orders

AbstractFor three types of triples: unordered, cyclic and transitive, the corresponding extended triple, extended triple system and their large sets are introduced. The existence of LESTS(υ) and LEMTS(υ) were completely solved. In this paper, we shall discuss the existence problem of LEDTS(υ) and give the following conclusion: there exists an LEDTS(υ) for any even υ except υ=4. The existence of LEDTS(υ) with odd order υ will be discussed in another paper, we are working at it

The Law Library and Legal Research

This issue of the Research News continues a series on the University libraries, which began in 1965 with three consecutive issues on the General Library, the Undergraduate Library, and the Clements Library, respectively. In the present issue, devoted to the Law Library, we will attempt to place the Library in the perspective of the discipline that it serves. To do this, we shall briefly discuss legal research and indicate some of the reasons for its great value. We shall then show, in general, how law libraries serve legal researchers and, in particular, how the University\u27s Law Library is set up for service. Finally, we shall trace the development of legal research in the University\u27s Law School and give an indication of its current vigor and distinction

Holland City News, Volume 89, Number 24: June 16, 1960

Newspaper published in Holland, Michigan, from 1872-1977, to serve the English-speaking people in Holland, Michigan. Purchased by local Dutch language newspaper, De Grondwet, owner in 1888.https://digitalcommons.hope.edu/hcn_1960/1023/thumbnail.jp

RV Atalante Fahrtbericht/Cruise report HYDROMAR V (replacement of cuise MSM06/2) Toulon, France - Recife, Brazil, 04.12.2007 - 02.01.2008

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