[CITATION][C] Bs-sequences
AG D'yachkov, VV Rykov - Mathematical notes of the Academy of Sciences …, 1984 - Springer
AG D'yachkov, VV Rykov
Mathematical notes of the Academy of Sciences of the USSR, 1984•SpringerDefinition i. A sequence of natural numbers a (1), a (2),.... a (t), where i~ a (1)~ a (2)~ 9..~ a
(t)= N, is called a Bs-sequence of length t with maximum element N if all the C~-I sums of the
form a (]~) a (/~)...~-a (/8), where i~] i< J~~ 9 9 9</~~ t, are different from each other. Let N (s,
t) denote the minimum possible value of N for given s and t. The best of the known upper
bounds for N (s, t) is obtained with the help of the Bose theorem of the additive number
theory [2], where for t= 2 pa Bs-sequence with the maximum element N= 2 ps= ts is …
(t)= N, is called a Bs-sequence of length t with maximum element N if all the C~-I sums of the
form a (]~) a (/~)...~-a (/8), where i~] i< J~~ 9 9 9</~~ t, are different from each other. Let N (s,
t) denote the minimum possible value of N for given s and t. The best of the known upper
bounds for N (s, t) is obtained with the help of the Bose theorem of the additive number
theory [2], where for t= 2 pa Bs-sequence with the maximum element N= 2 ps= ts is …
Definition i. A sequence of natural numbers a (1), a (2),.... a (t), where i~ a (1)~ a (2)~ 9..~ a (t)= N, is called a Bs-sequence of length t with maximum element N if all the C~-I sums of the form a (]~) a (/~)...~-a (/8), where i~] i< J~~ 9 9 9
Let N (s, t) denote the minimum possible value of N for given s and t. The best of the known upper bounds for N (s, t) is obtained with the help of the Bose theorem of the additive number theory [2], where for t= 2 pa Bs-sequence with the maximum element N= 2 ps= ts is constructed. Hence for arbitrary s and t such that s< t we get the estimate
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