In this paper, a new method of construction of three and five level second order slope-rotatable designs (SOSRD) using two suitably chosen dissimilar incomplete block designs like balanced incomplete block designs and symmetrical unequal block arrangements with two unequal block sizes is developed. The method of construction of SOSRD by Victorbabu and Narasimham [11] is shown to be a particular...

MacNeish's conjecture was disproved by Parker (12) who showed that in certain cases N(v) > n(v) by proving that if there exists a balanced incomplete block (BIB) design with v treatments, A = 1, and block size k which is a prime power then N(v) > k — 2, and that this result can be improved to N(v) > k — 1, when the design is symmetric and cyclic. Parker's result though it did not disprove Euler...

We say that an A 2-code is optimum if it has the minimum cheating probabilities and the minimum sizes of keys. We rst show that an optimum A 2-code implies an aane-resolvable design. Next, we de-ne an aane-resolvable + BIBD design and prove that an optimum A 2-code is equivalent to an aane-resolvable + BIBD design.

Techniques and results of constructing balanced incomplete block designs from a Frobenius group were summarized in [2]. These techniques and results grew out of observing that the sets Na + b of a planar near-ring (N, +, .) usually have a geometric interpretation. This observation was first illustrated in [1]. In this same work, one notices that sometimes the sets N{a,-a} + b also have geometri...