MinT - Best Known (17, s)-Sequences in Base 3

Best Known (17, s)-Sequences in Base 3

(17, 27)-Sequence over F₃ — Constructive and digital

Digital (17, 27)-sequence over F₃, using

t-expansion [i] based on digital (15, 27)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]

(17, 42)-Sequence in Base 3 — Upper bound on s

There is no (17, 43)-sequence in base 3, because

net from sequence [i] would yield (17, m, 44)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (17, 171, 44)-net in base 3, but
  - extracting embedded OOA [i] would yield OOA(3¹⁷¹, 44, S₃, 4, 154), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 685027 211508 324515 777792 095033 732379 709657 564813 491328 565171 830353 981268 593042 103819 / 155 > 3¹⁷¹ [i]