Mosaics of combinatorial designs for information-theoretic security

We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and privacy amplification for secret key generation. The security functions are functional forms of mosaics of combinatorial designs, more precisely, of group divisible designs and balanced incomplete block designs. Every member of a mosaic is associated with a unique color, and each color corresponds to a unique message or key value. Every block index of the mosaic corresponds to a public seed shared between the two trusted communicating parties. The seed set should be as small as possible. We give explicit examples which have an optimal or nearly optimal trade-off of seed length versus color (i.e., message or key) rate. We also derive bounds for the security performance of security functions given by functional forms of mosaics of designs.

Nutrient Use Efficiency Indices in Maize Hybrid as A Function of Various Rates of NPK in Mid Hills of Nepal

Field experiments were conducted to evaluate yield and nutrient use efficiency in maize in response to various rates of nitrogen (N), phosphorus (P) and potassium (K) in silty clay loam soil of Khumaltar, Nepal during 2019 and 2020. Three factorial randomized complete block designs with 27 treatment combinations were used in experiments, which were repeated three times. Three factors were N levels (150, 180, 210 N kg ha-1), P levels (40, 60, 80 P2O5 kg ha-1), and K levels (40, 60, 80 K2O kg ha-1). The results recommend to revise fertilizer dose since N210 kg ha-1 and K2O 80 kg/ha were optimum for increased maize production with grain yields of 10.95 t ha-1 and 10.54 t ha-1, respectively. Partial factor productivity, partial nutrient budget, internal efficiency, physiological efficiency, recovery efficiency, and agronomic efficiency of NPK for hybrid maize were mostly influenced by nutrient levels. Application of higher rate of P and K fertilizer improved maize N efficiencies, and case was valid for P and K efficiencies. Maize was more responsive to N and K fertilizer and lower rate of P application limited efficient use of applied N and K. To increase overall NUE, we recommend to revise dose of fertilizer for hybrid maize under mid hill condition of Nepal.

Groups \(S_n \times S_m\) in construction of flag-transitive block designs

In this paper, we observe the possibility that the group \(S_{n}\times S_{m}\) acts as a flag-transitive automorphism group of a block design with point set \(\{1,\ldots ,n\}\times \{1,\ldots ,m\},4\leq n\leq m\leq 70\). We prove the equivalence of that problem to the existence of an appropriately defined smaller flag-transitive incidence structure. By developing and applying several algorithms for the construction of the latter structure, we manage to solve the existence problem for the desired designs with \(nm\) points in the given range. In the vast majority of the cases with confirmed existence, we obtain all possible structures up to isomorphism.

Some notes on planning plant protection research in block designs with nested rows and columns

Summary Factorial experiments in block designs with nested rows and columns are described with suggestions about how they should be planned. In such experiments the importance of interaction and hidden replication are emphasized. Such experiments are carried out on heterogeneous experimental material. Thus, it is reasonable to seek a design that can withstand the loss of observations. The robustness of a block design with nested rows and columns against the loss of whole blocks is presented, along with examples of such designs.

Evaluation of AV-5055 as Seed Dresser in Lowland Rice Production

This experiment was established in 2020 cropping season at National Cereals Research Institute experimental field at Badeggi in Guinea Savannah agro-ecological Zone, (Latitude 9 040 Longitude 6 070 E), to assess seed dressing effect of AV-5055 on rice seed. The experiment was laid out in Randomized Complete Block Designs (RCBD), replicated three times. It consisted of four (4) treatments: application of AV-5055 rate at 0.7L, 1.2L, 1.7L per 100kg of rice seed and no application of chemical as (control). Data was taken on plant height, tiller count, days to 50% flowering, bird damage, rodent damage panicle per meter square and grain yield. The result shows that there was no significant difference (P > 0.05) in plant height, tiller count, days to 50% flowering and bird damage. However, control plot had significantly (P < 0.05) lower rodent damage (0.00) and higher grain yield (2060.00kg/ha) compared to rodent damage and grain yield in treated plots (0.33-2.33) and (1789.00-1999.03) respectively. It was concluded from the result of analysis that AV-5055 offer protection to dressed seed against bird depredation from planted field as there was no significant difference on bird depredation among the various rates of AV-5055 application. However, various rates of AV-5055 application attract picking by rodents and subsequent reduction on yield. Thus it was recommended that AV-5055 should be applied in combination with rodenticides to give perfect seed protection against birds and rodents.

Optimal Incomplete-Block Designs with Low Replication: A Unified Approach Using Graphs

An incomplete-block design defines both a concurrence graph and a Levi graph. Properties of either graph can be used to compare designs with respect to D-optimality and with respect to A-optimality. In this paper, we show that optimality of the design implies strong conditions on connectivity properties of the graph, and use this to classify the optimal designs when the number of observational units is close to minimal.