Most Robust BIBDs

New combinatorial designs and their applications to authentication codes and secret sharing schemes

This paper introduces three new types of combinatorial designs, which we call external difference families (EDF), external BIBDs (EBIBD) and splitting BIBDs. An EDF is a special type of EBIBD, so existence of an EDF implies existence of an EBIBD. We construct optimal splitting A-codes by using EDF. Then we give a new bound on the number of shares required in robust secret sharing schemes (i.e.,...

Existence of doubly near resolvable (v, 4, 3) BIBDs

The existence of doubly near resolvable (v, 2, 1)-BIBDs was established by Mullin and Wallis in 1975. For doubly near resolvable (v, 3, 2)-BIBDs, the existence problem was investigated by Lamken in 1994, and completed by Abel, Lamken and Wang in 2007. In this paper, we look at doubly near resolvable (v, 4, 3)-BIBDs; we establish that these exist whenever v ≡ 1 (mod 4) except for v = 9 and possi...

Some new near resolvable BIBDs with k=7 and resolvable BIBDs with k=5

Balanced Nested Designs and Balanced n-ary Designs

We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (1972). By use of these constructions, we show some constructions for regu...

Permutation approach for adjusted Durbin rank test used in balanced incomplete block designs for tied data

Durbin's rank test is widely used for testing treatment effects in Balanced Incomplete Block Designs (BIBDs) which have wide applications in sensory analysis. This test is failed for BIBDs when ties data occur. An adjusted version of Durbin rank test for this kind of data is given to solve this problem. Chi-square approximation, which is commonly used for this test, is not adequate for small BI...