Abstract
AbstractWe show that the necessary conditions for the existence of group divisible designs with block size four (4‐GDDs) of type are sufficient for (mod ), = 39, 51, 57, 69, 87, 93, 111, 123 and 129, and for = 13, 17, 19, 23, 25, 29, 31 and 35. More generally, we show that for (mod 6), the possible exceptions occur only when , and there are no exceptions at all if has a divisor such that (mod 4) or is a prime not greater than 43. Hence, there are no exceptions when (mod 12). Consequently, we are able to extend the known spectrum for and 5 (mod 6). Also, we complete the spectrum for 4‐GDDs of type .
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