✦ LIBER ✦
Proof of Williams' Conjecture on Experimental Designs Balanced for Pairs of Interacting Residual Effects
✍ Scribed by Harald Niederreiter
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 126 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
E. J. Williams conjectured that for every prime power (v \geqslant 3) there exists a (v(v-1) \times v) design balanced for pairs of interacting residual effects, and he proved this conjecture for the case in which (v) is a prime. Later, this conjecture was verified for (v \leqslant 64) by machine calculations. We prove the conjecture of Williams by a construction based on maximal period sequences in the finite field (G F(v)) and on certain complete sets of orthogonal latin squares.