MinT - Best Known (9, s)-Sequences in Base 3

Best Known (9, s)-Sequences in Base 3

(9, 18)-Sequence over F₃ — Constructive and digital

Digital (9, 18)-sequence over F₃, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
- an explicitly constructive algebraic function field [i]

(9, 25)-Sequence in Base 3 — Upper bound on s

There is no (9, 26)-sequence in base 3, because

net from sequence [i] would yield (9, m, 27)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (9, 77, 27)-net in base 3, but
  - extracting embedded OOA [i] would yield OOA(3⁷⁷, 27, S₃, 3, 68), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 147 808829 414345 923316 083210 206383 297601 / 23 > 3⁷⁷ [i]