MinT - Best Known (9, s)-Sequences in Base 4

Best Known (9, s)-Sequences in Base 4

(9, 21)-Sequence over F₄ — Constructive and digital

Digital (9, 21)-sequence over F₄, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
- an explicitly constructive algebraic function field [i]

(9, 25)-Sequence over F₄ — Digital

Digital (9, 25)-sequence over F₄, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
- Drinfeld modules of rank 1 [i]

(9, 36)-Sequence in Base 4 — Upper bound on s

There is no (9, 37)-sequence in base 4, because

net from sequence [i] would yield (9, m, 38)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (9, 110, 38)-net in base 4, but
  - extracting embedded OOA [i] would yield OOA(4¹¹⁰, 38, S₄, 3, 101), but
    - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 33 699933 333938 299743 333768 858774 538342 046430 528175 715601 379512 811520 / 17 > 4¹¹⁰ [i]