On the Existence of |
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| Authors: | Lijun Ji Yun Li |
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| Affiliation: | Department of Mathematics, Soochow University, Suzhou, China |
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| Abstract: | Let  there is an  . For  or  ,  has been determined by Hanani, and for  or  ,  has been determined by the first author. In this paper, we investigate the case  . A necessary condition for  is  . It is known that  , and that there is an  for all  with a possible exception  . We need to consider the case  . It is proved that there is an  for all  with an exception  and a possible exception  , thereby,  . |
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| Keywords: | t‐wise balanced design s‐fan design candelabra t‐system |
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there is an 
. For 
or 
, 
has been determined by Hanani, and for 
or 
, 
has been determined by the first author. In this paper, we investigate the case 
. A necessary condition for 
is 
. It is known that 
, and that there is an 
for all 
with a possible exception 
. We need to consider the case 
. It is proved that there is an 
for all 
with an exception 
and a possible exception 
, thereby, 
.