On t ‐designs and s ‐resolvable t ‐designs from hyperovals

Some Block Designs Constructed from Resolvable Designs

LetD be a resolvable 2−(v, k, λ) design, andD′ be a 2−(v′, k′, λ′) design, such that v′ = v k . Further, let r and r′ be replication numbers of a point in D and D′, respectively. Shrikhande and Raghavarao proved that then there exists a 2 − (v′′, k′′, λ′′) design D′′, such that v′′ = v, k′′ = kk′ and λ′′ = r′λ + (r − λ)λ′. If D′ is resolvable, then D′′ is also resolvable. Applying this result, ...

Constructing t-designs from t-wise balanced designs

We give a construction to obtain a t-design from a t-wise balanced design. More precisely, given a positive integer k and a t(v, {k1, k2, . . . , ks}, λ) design D, with with all block-sizes ki occurring in D and 1 ≤ t ≤ k ≤ k1 < k2 < · · · < ks, the construction produces a t-(v, k, nλ) design D∗, with n = lcm( ( k1−t k−t ) , . . . , ( ks−t k−t ) ). We prove that Aut(D) is a subgroup of Aut(D∗),...

On Euclidean t-designs

A Euclidean t-design, as introduced by Neumaier and Seidel (1988), is a finite set X ⊂ Rn with a weight function w : X → R+ for which

Abstract hyperovals and Hadamard designs

hyperovals and Hadamard designs

New t-designs and large sets of t-designs