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- W2042364920 abstract "A balanced incomplete block (BIB) design with $b$ blocks is said to have the support size $b^ast$ when exactly $b^ast$ of the $b$ blocks are distinct. BIB designs with $b^ast < b$ have interesting applications in design of experiments and controlled sampling as explained in details in Foody and Hedayat (1977) and Wynn (1977). A method called trade-off is introduced for the construction of BIB designs with repeated blocks. This method is utilized to study BIB designs with arbitrary $v$ treatments in blocks of size $k = 3$ in general and with $v = 7$ and $k = 3$ in particular. It is shown that BIB designs with $v = 7, k = 3$, any $b$, and any $b^ast$ exist if and only if (i) $b$ is divisible by 7, (ii) $7 leqslant b^ast leqslant min(b, 35)$, (iii) $b^ast neq 8, 9, 10, 12$, or $16$, (iv) $(b, b^ast) neq (28, 24), (28, 27), (35, 30), (35, 32), (35, 33), (35, 34)$ or (42, 34)." @default.
- W2042364920 created "2016-06-24" @default.
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- W2042364920 date "1979-11-01" @default.
- W2042364920 modified "2023-09-24" @default.
- W2042364920 title "The Trade-Off Method in the Construction of BIB Designs with Variable Support Sizes" @default.
- W2042364920 doi "https://doi.org/10.1214/aos/1176344846" @default.
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