On balanced incomplete-block designs with repeated blocks

On balanced incomplete-block designs with repeated blocks

Balanced incomplete-block designs (BIBDs) with repeated blocks are studied and constructed. We continue work initiated by van Lint and Ryser in 1972 and pursued by van Lint in 1973. We concentrate on constructing (v, b, r, k, λ)-BIBDs with repeated blocks, especially those with gcd(b, r, λ) = 1 and r ≤ 20. We obtain new bounds for the multiplicity of a block in terms of the parameters of a BIBD...

Variance Balanced Block Designs with Repeated Blocks

Some construction methods of the variance balanced block designs with repeated blocks are given. They are based on the incidence matrices of the balanced incomplete block designs with repeated blocks.

Block designs with repeated blocks

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Splitting balanced incomplete block designs

Remarks on Balanced Incomplete Block Designs

Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...