In 2001, the United Kingdom Engineering and Physical Sciences Research Council awarded three of the authors of this paper a grant for “A Web-based resource for design theory”. As the project developed, we have had to face a number of problems, ranging from fundamental questions such as “What is a design?”, through research topics such as “How should the concept of partial balance be extended to...

In this paper, we use the known recursive construction methods to obtain some new existence results for large sets of t-designs of prime sizes. We also present a new recursive construction which leads to more comprehensive theorems on large sets of sizes two and three. As an application, we show that for infinitely many values of block size, the trivial necessary conditions for the existence of...

This article present a application of Block Korkin---Zolotarev lattice reduction method for Lattice Reduction---Aided decoding under MIMO---channel. We give a upper bound estimate on the lattice reduced by block Korkin---Zolotarev method (BKZ) for different value of the block size and detecting by SIC.

There are well known necessary conditions for the existence of a generalized Bhaskar Rao design over a group G, with block size k = 3. We prove that they are sufficient for nilpotent groups G of even order, and in particular for 2-groups. In addition, we prove that they are sufficient for semi-dihedral groups.

Let X[0..n− 1] and Y [0..m− 1] be two sorted arrays, and define the m × n matrix A by A[j][i] = X[i] + Y [j]. Frederickson and Johnson [7] gave an efficient algorithm for selecting the kth smallest element from A. We show how to make this algorithm IO-efficient. Our cache-oblivious algorithm performs O((m + n)/B) IOs, where B is the block size of memory transfers.

We give some constructions of new infinite families of group divisible designs, GDD(n, 2, 4; 1, 2), including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for 3 n 8. For n= 10 there is one missing critical design. If 1> 2, then the necessary conditions are sufficient for n ≡ 4, 5, 8 (mod 12). For each of n=10, 15, 16, 17, 18, 19, and 20 we...

In this paper, we complete the existence of near generalized balanced tournament designs (NGBTDs) with block size 3 and 5. As an application, we obtain new classes of optimal constant composition codes.

The necessary conditions for the existence of a (2 × 4, λ)-splitting GDD of type g are gv ≥ 8, λg(v−1) ≡ 0 (mod 4), λg2v(v−1) ≡ 0 (mod 32). It is proved in this paper that these conditions are also sufficient except for λ ≡ 0 (mod 16) and (g, v) = (3, 3).

In Bitcoin system, transactions are prioritized according to attributes such as the remittance amount and transaction fees, and transactions with low priority are likely to wait for confirmation. Because the demand of micro payment in Bitcoin is expected to increase due to low remittance cost, it is important to quantitatively investigate how the priority mechanism of Bitcoin affects the transa...

We present a new approach to multiresolution vector quantisation. Its main advantage is exploitation of long-range correlations in the image by keeping vector size constant, independent of the image scale. We also developed a variable block-rate version of the algorithm, which allows better utilisation of the available bit budget by re ning only those areas of the image which are not e ciently ...