MinT - Best Known (12, s)-Sequences in Base 4

Best Known (12, s)-Sequences in Base 4

(12, 27)-Sequence over F₄ — Constructive and digital

Digital (12, 27)-sequence over F₄, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
- an explicitly constructive algebraic function field [i]

(12, 28)-Sequence over F₄ — Digital

Digital (12, 28)-sequence over F₄, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 29, using
- a curve from the manYPoints database [i]

(12, 46)-Sequence in Base 4 — Upper bound on s

There is no (12, 47)-sequence in base 4, because

net from sequence [i] would yield (12, m, 48)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (12, 140, 48)-net in base 4, but
  - extracting embedded OOA [i] would yield OOA(4¹⁴⁰, 48, S₄, 3, 128), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 124 330809 102446 660538 845562 036705 210025 114037 699336 929360 115994 223289 874253 133343 883264 / 43 > 4¹⁴⁰ [i]